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UNIVERSITY   OF   CALIFORNIA 


DEPARTMENT  OF  EDUCATION 


No. 


S 


A.   P.   Lange 


Education  Departraent 


"1 

! 


EATIO:NAlL^^i-iiV. 


Elementary    Arithmetic 


BY 

H.  II.  BELFIELD,  A.M.,  Ph.  D. 

DIRECTOR  OF  THE  CHICAGO  MANUAL  TRAINING  SCHOOL 

AND 

SARAH  C.   BROOKS 

SUPERVISOR  OF  PRIMARY  GRADES,   ST.  PAUL,  MINNESOTA 


CHICAGO 
SCOTT,  FORESMAN  AND  COMPANY 

1903 


f         r 


Copyright  1898.  1899 
Ey  SCOTT,.  FORESMAN  AND  COMl'ANY 


ROBT.     O.     IiAV     CO.,    PRrNTBlKS    A.N'D    BI^'CKKS,    OHICAUO. 


,   ,     J    )  J 


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PREFACE. 

The  product  of  the  latest  tlioiight  in  number  teaching  is 
fairly  represented  in  the  writings  of  Commissioner  W.  T.  Harris, 
in  the  reports  of  the  Committee  of  Ten  and  the  Committee  of 
Fifteen,  and  in  McLellan  and  Dewey's  "Psychology  of  Number." 
The  attempt  to  make  a  book  in  which  the  theory  of  these  educa- 
tors shall  be  wrought  into  a  practical  scheme  of  instruction  may 
well  call  forth  the  greatest  skill  and  most  serious  efforts  of  any 
author.  To  this  task  the  writers  of  this  book  have  set  their  hands, 
and  the  teaching  public  must  say  how  well  they  have  succeeded. 

The  arrangement  of  the  number  work  for  the 

ORDER  OF       elementary  grades  should  be  determined  by  the 

DEVELOPMENT.   Order  of  the  child's  mental  development  rather 

than  by  the  logic  of  the  subject  itself.  This 
requires  a  progressive  arrangement  of  all  material,  thereby  secur- 
ing a  proper  sequence  of  processes,  and  a  careful  grading  of  exer- 
cises. The  young  child  is  more  susceptible  to  likenesses  than  to 
differences.  His  judgments  and  classifications  are  therefore  hasty 
and  inexact.  Before  he  can  make  sharp  distinctions,  he  must  first 
have  the  means  at  hand  to  observe,  and  guidance  in  forming 
approximate  judgments  of  length,  width,  and  size  of  objects  con- 
trasted and  comj^ared.  Froebel  lays  great  stress  upon  this  phase 
of  early  training.  He  says:  "Every  external  object  comes  to  man 
with  the  invitation  to  determine  its  nature  and  relationships,  and 
everything  comes  to  be  known  only  as  it  is  connected  with  the 
opposite  of  its  kind.  The  first  law  of  all  phenomena  is  the  law  of 
opposites  or  contrast." 

The  use  of  color  in  the  lines  and  squares  in  the  early  part  of 
this    book    is   for    assistance   in    this    work    of    comparison    and 

V 


'  lyi  '\        '..:•::;  PREFACE. 

;  c0iitta§t./ 'Pages.?  to  11  provide  for  this  early  indefinite  compari- 
ison,  and  also  suggest  other  varieties  of  the  same  kind  of  work. 

The  idea  of  number  and  of  numerical  opera- 
MATERiAL.       tious  should  be  acquired  from  the  concrete.      Dr. 

Harris  in  the  introduction  to  the  "Psychology  of 
Number"  says,  "The  first  lessons  in  arithmetic  should  be  based 
on  the  practice  of  measuring  in  its  varied  applications."  The 
Committee  of  Ten  says,  "The  fundamental  operations  of  arith- 
metic should  not  only  be  j)erformed  symbolically  by  numbers, 
but  practically  by  joining  lines  together,  dividing  them,  etc." 
This  appeal  to  the  concrete  involves  the  use  of  certain  materials, 
and  any  successful  book  based  on  this  method  of  instruction 
must  provide  these  in  the  book  itself.  This  the  Rational  Arith- 
metic does  in  great  variety:  e.  g.,  colored  lines  and  squares; 
the  various  schemes  for  graphic  illustration  and  for  number  com- 
binations,— such  as  the  multiplication  tables  on  pages  64,  107,  etc.; 
the  construction  of  figures  for  linear  and  square  measure  on  pages 
101,  120,  etc.;  the  visual  presentation  of  fractions  on  pages  178, 
250,  etc.  By  means  of  these  the  child  is  also  trained  to  make  use 
of  other  material  which  will  aid  him  in  grasping  the  principles 
involved. 

In  this  book  the  early  presentation  of  number 
THE  UNIT.        is    made    by    the    use    of  the  quantitative,    and 

therefore  definite,  unit,  as  against  the  qualita- 
tive unit,  or  individual.  That  is,  the  use  of  lines,  of  inch,  cent, 
pint,  pound,  is  not  like  the  use  of  toothpicks,  a  mere  assembling 
of  individual  things,  but  a  measuring  of  quantities;  and  number  is 
essentially  a  development  of  quantity.  For  example,  by  joining 
lines  together  the  child  learns  that  four  is  equal  to  four  ones,  three 
and  one  or  one  and  three,  and  two  and  two  or  two  twos.  Moreover, 
the  child  learns  that  one  is  one-fourth  of  four,  and  that  two  are 
one-half  of  four,  thus  learning  his  fractions  along  with  his 
integers.  The  child  learns  these  facts  by  joining  lines  together; 
that  is,  he  not  only  learns  the  facts  from  the  book,  but  he 
knows  them  as  a  result  of  actual  experiment.  At  first  all  the 
lines  or  surfaces  used  should  be  actual  measurements,  so  that  the 


PREFACE.  vii 

child  will  learn  by  observation  to  apply  at  sight  the  information 
which  he  first  acquires.  This  measuring  of  lines  bears  the  same 
relation  to  the  kind  of  work  usually  given  that  the  laboratory 
experiment  bears  to  the  lecture.  The  boy,  not  the  teacher,  joins 
the  lines  together  for  the  same  reason  that  the  student  performs 
his  experiment  in  physics  for  himself. 

He  is  next  led  to  apply  his  facts  to  other  concrete  problems, 
such  as :  If  John  has  one  marble  and  Henry  has  three,  how  many 
have  both?  which  are  not  constructive,  but  which  oblige  him  to  use 
his  judgment.  Finally  the  number  combinations  thus  learned 
and  applied  are  fixed  by  a  series  of  drills.  An  essential  feature 
of  these  drill  tables  is  that  they  make  the  subject  less  formidable 
to  the  child.  For  example,  the  tables  on  page  43  show  that  if  the 
child  adds  three,  say,  to  a  series  of  numbers  ending  in  six,  all  the 
sums  will  end  in  nine.  As  soon  as  the  child  masters  the  develop- 
ment of  a  number,  he  is  taught  to  associate  it  with  certain  facts 
of  his  daily  life;  as,  for  example,  in  connection  with  the  number 
eight,  is  given  the  table  of  dry  measure,  and  with  the  number  twelve, 
the  foot,  the  months,  and  the  mysteries  of  the  clock  face.  In  this 
way  the  child  is  sure  to  be  interested,  and  his  powers  both  of 
memory  and  of  judgment  are  developed.  Throughout  the  book 
much  use  is  made  of  graphic  illustrations  and  concrete  problems, 
such  as  drawing  to  scale. 

The    problems    from    beginning   to   end   deal 
PROBLEMS.       with  realities,  and  aj^peal  so  far  as  possible  to  the 
child's  environment  or  experience.     This  gives  to 
the  work  an  interest  which  cannot   otherwise  be  secured,  and  cul- 
tivates the  power  of  observation  and  the  application  of  numbers  to 
every-day  objects  and  experiences. 

The  order  of  treatment  in  every  new  subject,  so  far  as  possible, 
has  been,  first,  to  give  the  concrete  form  which  will  present  the 
principle;  second,  to  give  the  abstract  principle  or  law  which 
has  been  illustrated;  and  lastly,  to  make  various  applications  of 
this  principle  in  a  series  of  problems  that  will  fix  the  knowledge 
of  number  relations  definitely  in  the  child's  mind. 


viii  PREFACE. 

The  authors  desire  to  make  special  acknowledgment  of  their 
indebtedness  to  the  many  superintendents,  principals,  and  teach- 
ers who  have  assisted  in  the  perfection  of  the  book  by  suggestions 
and  corrections  both  in  the  manuscript  and  proofs. 

The  Authors 


raTEODUCTION   FOR   TEACHEES 

Since  most  children  will  know  many  of  the 
PREFATORY,  number  facts  found  in  this  book  up  to  page  49, 
the  teacher  must  adapt  the  uses  of  these  pages  to 
the  needs  of  his  pupils.  If  they  have  but  little  knowledge  of  the 
simplest  combinations  up  to  12,  then  they  should  study  the  first 
part  of  the  book  very  slowly  and  carefully  until  these  number 
facts  are  thoroughly  fixed  in  mind.  If,  on  the  other  hand,  they 
are  familiar  with  most  or  all  of  the  combinations  of  these  49 
pages,  they  need  only  review  them  rapidly,  laying  stress  upon 
the  construction  and  the  acquiring  of  facility  in  the  number 
combinations,  such  as  those  on  pages  15,  23,  35,  41,  43,  etc. 

The  work  from  pages  7  to  11  supplies  ma- 
coMPARisoN.  terial  for  a  great  variety  of  indefinite  compari- 
sons, designating  the  objects  by  color.  From 
these  exercises  will  come  the  power  to  apply  readily  and  intelli- 
gently the  terms  longer,  shorter;  larger,  smaller;  higher  and 
loicer.  Through  the  definite  comparisons,  beginning  with  page 
12,  the  child  learns  to  answer  the  questions  Jioio  tniichf  hoio 
manyf  and  by  means  of  these  answers  develops  the  idea  of 
number  and  numerical  operations.  Interest,  judgment,  acts  of 
construction,  all  join  in  giving  the  child  knowledge  of  number 
and  power  to  use  it. 

Throughout  the   book  are  introduced  various 
CONSTRUCTION,   forms  of  constructive  work  such  as  the  drawing 

of  lines  and  rectangles  in  the  earlier  part  of 
the  book,  and  the  construction  problems  on  pages  101,  103, 
105,  122,  128,  188,  196,  etc.  These  not  only  add  variety, 
but  lead  to  increased  power  and  facility,  and  will  suggest  to  the 
teacher  other  forms  of  constructive  work  for  the  pupil.  If  pupils 
are  not  supplied  with  rulers,  the  teacher  may  show  them  how  to 

ix 


X         INTRODUCTION  FOR  TEACHERS. 

make  their  own.  Take  a  strip  of  heavy  paper  or  cardboard  and  cut 
it  the  length  of  the  green  line  on  page  18;  then  measure  from  one 
end  of  this  ruler  and  mark  on  it  the  length  of  each  line.  This 
will  give  a  six-inch  ruler  marked  in  inches.  By  means  of  the 
first  figure  on  page  178,  -^  and  ^  inches  may  also  be  marked. 

The  child's  natural  tendency  to  separate 
COUNTING.  wholes  into  parts  and  to  unite  the  parts  into 
wholes  again,  is  indicated  by  his  effort  in  count- 
ing by  ones.  This  natural  tendency  should  be  encouraged, 
as  it  is  a  means  of  gaining  facility  in  number.  The  counting 
table  on  page  42  should  be  worked  out  according  to  the  sugges- 
tions at  the  foot  of  the  page.  At  various  points  through  the  book 
pupils  should  be  trained  to  form  similar  counting  tables  by  2's, 
3's,  4's,  5's,  etc.  This  not  only  interests  the  child,  but  is  a  great 
aid  in  securing  skill  in  number  combinations. 

Great  effort  should  be  made  to  render  purely 

FUNDAMENTAL  automatic  the  fundamental  combinations.      The 

COMBINATIONS,  first  scrics  of  these  will  be  found  at  the  foot  of 

page  43.  Drills  on  the  others  are  frequent  and 
thorough,  beginning  with  the  material  on  page  108.  The 
remainder  of  the  45  fundamental  combinations  are: 

456567677889 
987987989899 

From  page  68  to  87   the  number  knowledge 
DENOMINATE    acquired   is   applied  to  the  simplest  form  of  de- 
NUMBEES.       nominate  numbers.     This  work  leads  the  child  to 
apply  the  numbers  already  learned  to  his  every- 
day experience,  by  becoming  familiar  with  a  few  simple  facts  of 
liquid  and  dry  measures,   weights,   money  and    time.     Children 
should  be  urged  to   construct  simple  problems  which  .will  apply 
these  facts  of  denominate  numbers. 

Great  care  should     be  taken    not   to    exceed 

FUNDAMENTAL   the   work    planned    in    the    fundamental    opera- 

OPERATioNS.     tions,  pages  88  to  100.     At  this  stage  the  child 

will  get  his   first   knowledge  of    the  formal  use 

of  these  operations,  and  only  the  simplest  forms  of  these  processes 


INTRODUCTION   FOR   TEACHERS.  xi 

should  be  taught.  In  the  second  part,  pages  164  to  177,  another 
step  is  taken  in  the  study  of  these  operations  and  the  same  caution 
still  applies.  The  final  treatment  is  found  on  pages  230  to  235_ 
and  there  the  child  should  be  required  to  master  these  truly 
fundamental  processes  of  the  science  of  arithmetic. 

The  plan  of  the  book  requires  constant  re- 
REViEWS.  views  of  the  work  that  has  previously  been  done. 
While  the  character  of  the  drills  and  problems  is 
such  that  necessarily  this  preceding  work  must  have  been  thor- 
oughly done,  still  the  teacher  should  not  fail  to  turn  frequently 
to  certain  pages  in  the  book  and  review  them  with  special  care. 
At  various  points  suggestive  reviews  are  indicated,  as  on  pages 
70,  130,  131,  146,  155,  etc. 

Too  much  attention  can  hardly  be  given  to  the 
ORAL  AVORK.  Oral  work  throughout  the  entire  book.  Many  of 
the  drill  tables  provide  abstract  number  work  of 
this  sort  and  the  teacher  should  see  that  such  work  is  done  orally. 
On  certain  images,  as  on  130,  131,  160,  161,  etc.,  a  division  of  the 
page  points  out  those  which  are  distinctly  oral  problems.  On 
many  other  pages  there  are  problems  which  may  be  solved  orally 
and  the  teacher  should  see  that  this  is  done,  determining  by 
the  advancement  of  the  j^^ipils,  which  should  be  oral  and  which 
written. 

In   both   oral  and  written    work  care   should 
FORMS  OF       be   taken    that   the    statements    of   problems   are 
STATEMENT,      clcar  and  concise.      The  following  examples  will 
serve  as  illustrations: 

examples: 

(a)  A  man  spends  $2.40  for  coffee,  80  cents  for  tea,  $2.50  for  flour,  $1.75 
for  butter,  and  $1  for  bacon.     What  is  the  amount  of  his  purchase? 

Statement:  The  amount  of  his  purchase  is  the  sum  of  82.40,  80c,  $2.50, 
$1.75,  and  $1,  which  is  $8.45. 

(&)    What  change  should  he  receive  from  $10? 

Statement:  He  should  receive  the  difference  between  $10  and  $8.45, 
which  is  $1,55. 

(c)    At  $85  a  head,  what  will  96  horses  cost? 

Statement:    96  horses  will  cost  96  times  $85,  or  $8,160. 

(cV)  In  an  orchard  of  156  trees  there  are  12  rows.  How  many  trees  in 
a  row? 


xli  INTRODUCTION   FOR   TEACHERS. 

Statement:     There  are  as  many  trees  as  there  are  12's  in  156,  or  13. 
(d-)     Divide  96  marbles  equally  among  8  boys. 
Statement:     Each  boy  will  receive  }^  of  96  marbles,  or  12  marbles. 
Brief  written  statements  should  also  be  made  from  time  to  time,  from 
the  beginning  of  the  4th  year,  of  problems  in  multiplication  and  division; 
e.  g.: 

1. 
$85=: cost  of  one  horse. 
96=rnumber  to  be  bought.  2. 

156=number  of  trees. 

510  12=         "  rows. 

765  156.-4-12=13,    "  in   each  row. 


$8160=cost  of  96  horses. 

3. 
96=whole  number  of  marbles. 
8=number  of  boys  to  receive  equal  number. 
%  of  96--- 12,  number  of  marbles  each  boy  receives. 


kSakah  C.   Brooks. 


CONTENTS. 

PAGE. 

Preface,  ..-.-----v 

Introduction  for  Teachers,        ------  ix 

PART   FIRST. 

Indefinite  Comparison: 

With  Lines,         -            -            - 7 

With  Surfaces,          ..--.-'  9 

With  Solids, -            -            -  10 

With  General  Objects,        ------  11 

Definite  Comparison   with  Lines:    Linear   Measure  (Numbers   from 

4  to  12),    - 12 

Counting  Table  (jNotation  and  Numeration),.-            -     .        -            -  42 

Fundamental  Combinations,           -            -            -            -            -            -  43 

DoHnite  Comparison  with  Surfaces:  Square  Measure  (Numbers  from 

1  to  24),          --------  44 

Multiplication  by  5.              -            -            -            -            -            -           -  65 

Drill  Tables  on  Numbers  from  2  to  60,            -            -            -            -  66 

Definite  Comparison  with  Solids:  Cubic  Measure,          -            -            -  68 

Liquid  Measure,               -...--.  74 
Dry  Measure,             ...-----76 

Weights,  -.----.--  78 

United  States  Money,           ....-.-  80 

Time,        - -            -            -  82 

Fundamental  Operations: 

Addition, 88 

Subtraction,             -            -            .            .            -            .            -  93 

Multiplication,    --------  95 

Division  (Short), 97 

PART  SECOND. 

Linear  Measure,        .---.-.-  101 

Multiplication  by  6,        -            -            -            -           -           -           -  106 

xiii 


XIV  CONTENTS. 

PAGE. 

Square  Measure,        --------  HI 

Multiplication  by  7,        -  -  -  -  -  -  -  116 

Areas  of  Triangles,  .--.-.-  120 

Multiplication  by  8,        -  -  -  -  -  -  -  124 

Cubic  Measure,         -  -  -  -  -  -  -  -  128 

Multiplication  by  9,        -  -  -  -  -  -  .134 

Weights, -  -  -  140 

Multiplication  by  10,      -  -  -  -  -  -  -  142 

United  States  Money,  -  -  -  -  -  -  -  146 

Multiplication  by  11,      -  -  -  ^  -  -  -  148 

Multiplication  by  12, 152 

Time,        ---------  156 

Writing  and  Reading  Numbers  (Notation  and  Numeration),     -  -  162 

Fundamental  Operations: 

Addition,  -  _ 164 

Subtraction,  -------  168 

Multiplication,   -  -  -  -  -  -  -  -  172 

Division  (Short),      -------  176 

Fractions  (Common),  -------  178 

PART  THIRD. 

Linear  Measure,        --------  185 

Combinations  of  123^^,    - 190 

Division  (Long),        --------  197 

Square  Measure,  .--._--  200 

Combinations  of  13,  -  -  -  -  -  -  -  204 

Combinations  of  14,        -  -  -  -  -  -  -  207 

Areas  of  Triangles,   --------  209 

Cubic  Measure,  -  -  -  -  -  -  .  -  214 

Combinations  of  15,  -  -  -  -  -  -  -  218 

Liquid  Measure, 220 

Combinations  of  16,  -  -  -  -  -  -  -  222 

Dry  Measure,       --------  224 

Combinations  of  16^,  -------  226 

Notation  and  Numeration:   Arabic  and  Roman,        -  .  -  228 


CONTENTS. 


XV 


Fundamental  Operations: 

Addition, 

Subtraction, 

Multiplication, 

Division  (Long), 
Combinations  of  20, 
Weights, 
Time, 

United  States  Money, 
Paper  Measure,   - 
Fractions  (Common), 
Denominate  Numbers,   - 
Bills,   - 

Fractions  (Decimal), 
Percentage,    - 


PAGE. 

230 

-  231 
232 

-  234 
237 

-  238 
240 

-  244 
245 

.  250 
254 

•  258 
262 

.    264 


J    1 

5      » 


>     3 
3      » 


,     J    0    >    .> 


'      ,     J  J  5     0     ,  '  -.  '      >        '     ■>         ' 


PART   FIRST. 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 
10, 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 


The  red  line  is  longer  than  which  line  ? 
The  orange  line  is  shorter  than  which  line  ? 
The  yellow  line  is  shorter  than  which  line? 
The  green  line  is  longer  than  which  line  ? 
The  purple  line  is  shorter  than  which  line  ? 
The  blue  line  is  longer  than  which  line  ? 
Which  line  is  longer  than  the  red  line  ? 
Which  lines  are  shorter  than  the  red  line  ? 
Which  lines  are  longer  than  the  orange  line? 
Which  lines  are  shorter  than  the  orange  line  ? 
Which  lines  are  longer  than  the  yellow  line? 
Which  lines  are  longer  than  the  green  line  ? 
Which  lines  are  shorter  than  the  green  line  ? 
Which  lines  are  longer  than  the  ]3urple  line  ? 
Which  lines  are  shorter  than  the  purple  line? 
Which  lines  are  shorter  than  the  blue  line  ? 
Is  any  one  of  these  lines  longer  than  the  blue  line? 
Is  any  one  shorter  than  the  yellow  line  ? 

7 


->^'' 


THE  RATIONAL  ARITHMETIC. 


1. 
2. 

3. 
4. 
5. 
6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 

!    ; 

i    15. 

16. 
17. 
18. 


"Whicli  line  is  longest? 

Whicli  line  is  next  longest?  • 

Which  line  is  shortest? 

What  line  is  next  shortest  ? 

The  red  line  is  longer  than  which  line? 

The  red  line  is  shorter  than  which  lines  ? 

The  green  line  is  longer  than  which  lines  ? 

The  green  line  is  shorter  than  which  lines  ? 

The  blue  line  is  longer  than  which  lines  ? 

The  blue  line  is  shorter  than  which  lines  ? 

The  orange  line  is  longer  than  which  lines  ? 

The  orange  line  is  shorter  than  which  line  ? 

Two  lines  are  equal,  which  are  they  ? 

How  many  of  these  lines  are  longer  than  the  yellow 

line? 
How  many  of  these  lines  are  longer  than  the  red  line  ? 
How  many  of  these  lines  are  longer  than  the  green 

line? 
How  many  of  these  lines  are  shorter  than  the  orange 

line? 
How  many  of  these  lines  are  shorter  than  the  purple 

line? 


PART   FIRST. 


9 


/ 


liijjjiiiijfi,, . 


■^tiy 


1.  WMcli  two  squares  are  tlie  largest? 

2.  WMcli  two  squares  are  tlie  smallest? 

3.  The  blue  square  is  larger  than  wliicli  squares? 

4.  The  orange  square  is  smaller  than  which  square  ? 

5.  The  orange  square  is  larger  than  which  squares? 

6.  The  green  square  is  larger  than  which  squares? 

7.  The  green  square  is  smaller  than  which  squares? 

8.  The  purple  square  is  smaller  than  which  squares? 

9.  The  yellow  square  is  larger  than  which  square? 

10.  The  yellow  square  is  smaller  than  which  squares? 

1 1 .  The  red  square  is  larger  than  which  squares  ? 

12.  How  many  squares  are  larger  than  the  red  square? 

How  many  are  smaller  ? 
18.  How  many  squares  are  smaller  than  the  green  square  ? 

How  many  are  larger  ? 
14.  How  many  squares  are  larger  than  the  pur^^le  square  ? 

How  many  are  smaller  ? 
f^.  How  many  squares  are  larger  than  the  yellow  square  ? 


10 


THE  RATIONAL  ARITHMETIC. 


"^<!k" 


1.  WMcli  is  the  largest  cube? 

2.  Wliicli  is  the  next  largest  cube? 

3.  Wliicli  is  tlie  smallest  cube? 

4.  Wliicli  is  the  next  smallest  cube  ? 

5.  The  red  cube  is  larger  than  which  cubes? 

6.  The  green  cube  is  larger  than  which  cubes? 

7.  The  green  cube  is  smaller  than  which  cubes? 

8.  The  blue  cube  is  larger  than  which  cube? 

9.  The  blue  cube  is  smaller  than  which  cubes? 

10.  The  purple  cube  is  larger  than  which  cubes? 

11.  The  purple  cube  is  smaller  than  which  cube? 

12.  The  orange  cube  is  smaller  than  which  cubes? 

13.  The  orange  cube  is  larger  than  which  cubes? 

14.  The  yellow  cube  is  smaller  than  which  cubes? 

15.  How  many  cubes  are  smaller  than  the  orange  cube? 

16.  How  many  cubes  are  larger  than  the  orange  cube? 

17.  How  many  cubes  are  smaller  than  the  purple  cube? 

18.  How  many  cubes  are  larger  than  the  23ur23le  cube? 

19.  How  many  cubes  are  smaller  than  the  green  cube? 

20.  How  many  cubes  are  larger  than  the  blue  cube? 


PART   FIRST.  11 

These  questions  should  all  be  answered  by  the  pupil  without  the  use  of 
a  ruler;  and  if  the  pupil  is  uncertain,  the  teacher  himself  should  answer 
without  measuring. 

1.  Whicli  is  longer,  the  window  or  the  door? 

2.  Which  is  wider,  the  door  or  the  window? 

3.  Which  is  higher,  your  desk  or  the  teacher's  desk  ? 

4.  Which  is  longer,  your  desk  or  the  teacher's  desk  ? 

5.  Is  the  top  of  the  blackboard  higher  than  the  top  of 

the  door? 

6.  Is  your  desk  farther  from  the  door  or  from  the 

teacher's  desk? 

7.  Which  is  longer,  your  pencil  or  your  penholder? 

8.  Is  a  piece  of  crayon  the  same  size  at  both  ends? 

9.  Which  is  larger,  your  slate  or  the  cover  of  your 

Arithmetic  ? 

10.  Which  is  thicker,  your  Arithmetic  or  your  slate? 

11.  Are  the  four  sides  of  your  slate  the  same  length? 

Are  any  two  sides  of  it  the  same  length  ^ 

12.  Which  is  larger,  your  house  or  the  school -house? 

Which  is  higher  ? 

13.  Which  is  wider,  the  sidewalk  in  front  of  the  school - 

house  or  that  in  front  of  your  house  ? 

14.  Which  is  wider,  the  street  in  front  of  the  school - 

house  or  that  in  front  of  your  house  ? 

15.  Which  is  farther  from  your  house,  the  store  or  the 

school  ? 

16.  Which  is  longer,  the  side  of  the  school-house,  or  the 

end  of  it  ? 

17.  Are  all  the  edges  of  a  brick  the  same  length? 

18.  Is  a  brick  longer  than  it  is  wide?     Is  is  thicker 

than  it  is  wide  ? 


42  THE  RATIONAL  ARITHMETIC. 


1 .  The  red  line  is  how  many  times  as  long  as  the  blue  line  ? 

2.  The  red  line  and  the  blue  line  equal  which  line? 

3.  The  purple  line  is  how  many  times  as  long  as  the 

blue  line  ? 

4.  The  purple  line  and  the  blue  line  equal  which  line  ? 

5.  The  red  line  and  which  line  equal  the  purple  line? 

6.  The  purple  line  and  which  line  equal  the  yellow  line  ? 

7.  If  from  the  purple  line  we  take  a  line  equal  to  the 

blue,  which  line  will  the  remainder  equal  ? 

8.  If  from  the  purple  line  we  take  a  line  equal  to  the 

red,  which  line  will  the  remainder  equal  ? 

9.  If  from  the  yellow  line  we  take  a  line  equal  to  the 

blue,  which  line  will  the  remainder  equal  ? 

10.  If  from  the  yellow  line  we  take  a  line  equal  to  the 

red,  which  line  will  the  remainder  equal  ? 

11.  If  from  the  yellow  line  we  take  a  line  equal  to  the 

purple,  which  line  will  the  remainder  equal  ? 

12.  The  blue  line  equals  what  part  of  the  red? 

13.  The  purple  line  is  how  many  times  as  long  as  the 

blue  line  ? 

14.  The  blue  line  equals  what  part  of  the  purple? 

15.  The  yellow  line  is  how  many  times  as  long  as  the 

blue  line? 

Note.— The  exercises  on  pages  12, 16,  20,  24  and  28  may  be  varied  by 
the  use  of  colored  sticks  or  by  colored  lines  upon  the  board,  drawn  the 
same  length  as  patterns  given  or  scaled  longer.  These  should  be  placed  in 
different  positions  so  as  to  test  judgment  further. 


PART  FIRST.  13 

1.  Tlie  blue  line  equals  what  part  of  the  yellow  line? 

2.  The  yellow  line  is  how  many  times  as  long  as  the 

red  line  ? 

3.  The  red  line  e(][uals  what  part  of  the  yellow  line? 

4.  The  yellow  line  is  equal  in  length  to  which  two 

other  lines  ? 

5.  The  purple  line  equals  what  part  of  the  yellow  line  ? 

6.  Two  times  the  blue  line  equals  which  line  ? 

7.  Three  times  the  blue  line  equals  which  line  ? 

8.  Four  times  the  blue  line  equals  which  line? 

9.  Two  times  the  red  line  equals  which  line? 

10.  What  is  the  length  of  the  blue  line  ?     Of  the  red  ? 

Of  the  purple  ?     Of  the  yellow  ? 

11.  2  inches  and  1  inch  are inches. 

12.  3  inches  and  1  inch  are inches.  ' 

13.  3  inches  equal  2  inches  and inch.   ' 

14.  4  inches  equal  2  inches  and inches. 

15.  3  inches  less  1  inch  are inches. 

16.  4  inches  less  2  inches  are inches. 

17.  4  inches  less  1  inch  are inches. 

18.  3  inches  less  2  inches  are inch. 

19.  4  inches  less  3  inches  are .  inch. 

20.  1  inch  is  what  part  of  3  inches  ? 

21.  2  inches  are  what  part  of  3  inches? 

22.  1  inch  is  what  part  of  4  inches? 

23.  2  inches  are  what  part  of  4  inches? 

24.  3  inches  are  what  part  of  4  inches  ? 

25.  3  inches  are  three  times inch. 

26.  1  inch  is  one -third  of inches. 

27.  3  inches  are  one  and  one-half  times inches. 

28.  2  inches  are  two -thirds  of inches. 


14  THE   RATIONAL   ARITHMETIC. 

1.  4  inclies  are  four  times incli, 

2.  1  incli  is  one-fourtli  of inches. 

3.  4  inclies  are  two  times inclies. 

4.  2  inches  are  one -half  of inches. 

5.  4  inches  are  one  and  one -third  times inches. 

6.  3  inches  are  three -fourths  of inches. 

7.  James  spent  2  cents  for  an  apple  and  for  an  orange 

2  cents  more  than  for  the  apple.     The  orange 
cost cents. 

8.  Helen  had  three  books.     Her  mother  gave  her  one 

more;  how  many  had  she  then? 

9.  Joe  sold  two  papers  and  John  sold  one;  how  many 

did  both  sell  ? 

10.  A  fence  is  four  feet  high  and  a  gate  in  it  is  one  foot 

lower;  how  high  is  the  gate? 

11.  At  one  cent  each,  what  will  three  apples  cost? 

12.  At  ^  cent  each,  what  will  four  apples  cost? 

13.  When  oranges  cost  2  cents  each,  how  many  can  be 

bought  for  4  cents  ? 

14.  Harry  lives  four  blocks  from  the  school-house,  and 

Bert  lives  one -half  as  far.     How  many  blocks  is 
it  from  Bert's  house  to  the  school -house? 

15.  A  girl  paid  4  cents  for  a  spool  of  thread  and  2  cents 

less  for  needles;  how  much  did  she  pay  for  the 
needles  ? 

16.  A  piece  of  crayon  four  inches  long  is  broken  into 

four  equal  parts;  how  long  is  each  part? 

17.  George  had  three  marbles  and  lost  one;  how  many 

did  he  then  have  ?     What  part  did  he  lose  ? 

18.  A  boy  bought  four  sticks  of  candy  and  ate  two  of 

them;  what  part  had  he  left? 


PART   FIRST.  15 

1.  Charlie  earned  3  cents  and  spent  1  cent  for  a  top; 

what  part  of  his  money  did  he  spend  ? 

2.  Mary  walks  four  blocks  to  school  and  Ethel  one- 

fourth  as  far;  how  many  blocks  does  Ethel  walk? 

3.  John  can  jump  four  feet  and  Charlie  one -half  as 

far;  how  many  feet  can  Charlie  jump? 

4.  Alfred  worked  3  days  and  Carl  one -third  as  many 

days;  how  many  days  did  Carl  work? 

5.  A  stick  is  three  feet  long,  a  piece  one  foot  long  is 

broken  off;  what  part  is  broken  off?     What  part 
is  left? 

6.  Combinations  for  Drill: 

Addition 


1 

2 

2 

1 

1 

2 

1 

2 

1 

3 

2 
1 

1 
1 

1 

1 

3 

2 

2 

1 

2 

• 

2 

• 

2 

m 

2 

• 

2 

• 

2 

4 

4 

4 

3 

3 

Subtraction 

4 

3 

2 

4 

4 

3 

2 

• 

• 

2 

• 

2 

• 

2 

• 

2 

• 

i  of  3=  i  of  4=  i  of  4- 

I  of  3=  I  of  4=  i  of  4= 


16 


THE   RATIONAL  ARITHMETIC. 


1.  The  red  line  is  how  many  times  as 
long  as  the  yellow  line  'i 

2.  The  red  line  and  the  yellow  line 
equal  which  line? 

3.  The  purple  line  is  how  many  times 
as  long  as  the  yellow  line  ? 

4.  The  orange  line  is  how  many  times 
as  long  as  the  yellow  line  ? 

5.  The  orange  line  and  the  purple  line 
equal  which  line  ? 

6.  The    yellow    line    and   which   line 
equal  the  blue  line? 

7.  The    orange    line    and   which   line 
equal  the  blue  line  ? 

8.  The   purple    line    and   which    line 
equal  the  blue  line  ? 

9.  The  red  line  and  which  line  equal 
the  blue  line? 

10.  If  from  the  blue  line  we  take  a  line 
equal  to  the  yellow,  which  line 
will  the  remainder  equal  ? 

11.  If  from  the  blue  line  we  take  a  line 
equal  to  the  orange,  which  line 
mil  the  remainder  equal  ? 

12.  If  from  the  blue  line  we  take  a  line 
equal  to  the  purple,  which  line 

will  the  remainder  equal  ? 
18.  If  from  the  blue  line  we  take  a  line  equal  to  the 

red,  which  line  mil  the  remainder  equal  ? 
14.  The  blue  line  is  how  many  times  as  long  as  the 

yellow  ? 


PART   FIRST.  r* 

1.  The  yellow  line  equals  what  part  of  the  blue? 

2.  The  blue  line  is  how   many  times  as  long   as  the 

orange  ? 

3.  The  orange  line  equals  what  part  of  the  blue? 

4.  The  blue  line  is  how  many  times  as  long  as  the 

]3urple  ? 

5.  The  purple  line  equals  what  part  of  the  blue? 

6.  The  blue   line  is  how  many  times  as  long   as  the 

red? 

7.  The  red  line  equals  what  part  of  the  blue? 

8.  What  is  the  length  of  the  yellow  line?      Of  the 

orange?     Of  the  purple?     Of  the  red?     Of  the 
blue? 

9.  A  boy  paid  2  cents  for  paper,  1  cent  for  a  penholder 

and  2  cents  for  pens ;  how  much  did  he  pay  for  all  ? 

10.  Helen  had  5  pennies.     She  gave  one  to  her  brother, 

and  lost  one;  how  many  had  she  left? 

11.  If  you  have  a  nickel  and  buy  a  top  for  3  cents,  how 

much  change  should  you  receive  ? 

12.  How  many  2 -cent  stamps  can  you  get  for  a  nickel? 

How  much  money  will  you  have  left  ? 

13.  Paul  had  ^ve  peaches.     He  ate  one,  how  many  had 

he  left?    He  gave  half  the  remainder  to  his  sister; 
how  many  did  he  give  her  ? 

14.  Charles  is  five  years  old  and  the  baby  is  one -fifth  as 

old;  how  old  is  the  baby? 

15.  Peter  had  5  dollars  and  bought  a  hat  for  2  dollars  ; 

what  part  of  his  money  did  the  hat  cost  ? 

16.  James  had  five  apples.     He  gave  one-fifth  of  them 

to  his  brother;   how  many  apples  had   he  leffc? 
What  part  had  he  left  ? 


18 


THE   RATIONAL   ARITHMETIC. 


1.  The  blue  line  is  how  many  times 

as  long  as  the  yellow? 

2.  The  blue  line  and  the  yellow  line 

equal  which  line? 

3.  The    purple    line    is    how   many 

times  as  long  as  the  yelloAv? 

4.  The  orange  line  is  how  many  times 

as  long  as  the  yellow? 

5.  The  orange  line  and  the  purple 

line  equal  which  line? 

6.  The  red  line  is  how  many  times 

as  long  as  the  yellow  ? 

7.  The  red  line  and  the  orange  line 

and  the  yellow  line  equal  which 
line? 

8.  The  yellow  line  and  which  line 

equal  the  green? 

9.  The  orange  line  and  which  line 

equal  the  green  ? 

10.  The   red    line   and   which    lines 

equal  the  green  ? 

11.  The  purple  line  and  which  line 

equal  the  green  ? 

12.  The   blue   line   and   which    line 

equal  the  green? 

13.  If  from  the  green  line  we  take  a 

line  equal  to  the  yelloAV,  which 
line  will  the  remainder  equal  ? 

14.  If  from  the  green  line  we  take  a 

line  equal  to  the  orange,  which 
line  will  the  remainder  equal  ? 


PART    FIRST.  19 

1.  If  from  the  green  line  we  take  a  line  equal  to  tlie 

red,  wliicli  line  will  tlie  remainder  equal  ? 

2.  If  from  the  green  line  we  take  a  line  equal  to  the 

purple,  wliicli  line  will  the  remainder  equal  ? 

3.  If  from  the  green  line  we  take  a  line  equal  to  the 

blue,  which  line  will  the  remainder  equal  ? 

4.  Three  times  the  yellow  line  equals  which  line? 

5.  Six  times  the  yellow  line  equals  which  line? 

6.  Two  times  the  red  line  equals  which  line? 

7.  The  green  line  is  two  times  as  long  as  which  line? 

8.  The  red  line  is  one-half  as  long  as  which  line? 

9.  Two  times  the  yellow  line  equals  which  line? 

10.  Six  times  the  yellow  line  equals  which  line? 

11.  Three  times  the  orange  line  equals  which  line? 

12.  The  green  line  is  three  times  as  long  as  which  line? 

13.  The  orange  line  is  one-third  as  long  as  which  line? 

14.  The  green  line  is  how  many  times  as  long  as  the 

yellow  ? 

15.  The  yellow  line  equals  what  part  of  the  green? 

16.  The  green  line  is  how  many  times  as  long  as  the 

orange  ? 

17.  The  orange  line  equals  what  part  of  the  green? 

18.  The  green  line  is  how  many  times  as  long  as  the  red  ? 

19.  The  red  line  equals  what  part  of  the  green? 

20.  The  green  line  is  how  many  times  as  long  as  the 

purple  ? 

21.  The  purple  line  e([uals  what  part  of  the  green? 

22.  The  green  line  is  how  many  times  as  long  as  the 

blue? 

23.  The  blue  line  equals  what  part  of  the  green? 

24.  What  is  the  length  of  the  yellow  line? 


20  THE   RATIONAL   ARITHMETIC. 

( See  figure  on  page  18.) 

1.  What  is  tlie  length  of  tlie  orange  line? 

2.  What  is  the  length  of  the  red  line  ? 

3.  What  is  the  length  of  the  j^urple  line? 

4.  What  is  the  length  of  the  bine  line  ? 

5.  What  is  the  length  of  the  green  line? 

6.  5  inches  and  1  inch  are__ inches. 

7.  4  inches  and  2  inches  are .  inches. 

8.  3  inches  and  3  inches  are  _^_____  inches. 

9.  6  inches  equal  1  inch  and inches. 

10.  6  inches  equal  3  inches  and inches. 

11.  6  inches  equal  5  inches  and inch. 

12.  6  inches  equal  2  inches  and  _^___^  inches. 

13.  6  inches  equal  4  inches  and inches. 

14.  6  inches  less  5  inches  are inch. 

15.  6  inches  less  3  inches  are inches. 

16.  6  inches  less  1  inch  are inches. 

17.  6  inches  less  4  inches  are  . .  inches. 

18.  6  inches  less  2  inches  are inches 

19.  1  inch  is  what  part  of  6  inches? 

20.  3  inches  are  what  part  of  6  inches  ? 

21.  5  inches  are  what  part  of  6  inches? 

22.  2  inches  are  what  part  of  6  inches? 

23.  4  inches  are  what  part  of  6  inches? 

24.  6  inches  are  two  times .  inches. 

25.  3  inches  are  one -half  of inches. 

26.  6  inches  are  three  times inches. 

27.  2  inches  are  one-third  of .  inches. 

28.  6  inches  are  one  and  one-half  times inches. 

29.  4  inches  are   two-thirds  of  ______^_  inches. 

30.  6  inches  aj*e  one  and  one -fifth  times inches. 


PART   FIRST.  n 

1.  5  inches  are  five -sixths  of inches. 

2.  Harry  had  a  nickel  and  a  penny;  how  many  cents 

had  he? 

3.  James  had   six   books  and  gave  away  two.     How 

many  books  had  he  left? 

4.  A  boy  earned  three  cents  one  day,  and  three  cents 

the  next  day ;  how  much  did  he  earn  in  both  days  ? 

5.  Helen  is  four  years  old,  and  her  sister  is  two  years 

older;  how  old  is  her  sister? 

6.  A  quart  of  milk  costs  six  cents;  how  much  does  half 

a  quart  cost  ?  * 

7.  A  boy  walked  two  miles  in  one  hour;  how  many 

miles  can  he  walk  in  three  hours  ? 

8.  There  are  six  stores  in  one  block  and  two -thirds  as 

many  in  the  next.     How  many  stores  are  there  in 
the  second  block? 

9.  Kobert  had  six  tops  and  lost  four.     What  part  did 

he  lose?     What  part  had  he  left? 

10.  Jessie  had  two  dolls,  which  were  one-third  as  many 

as  May  had;  how  many  had  May? 

11.  Mary  had  six  cents  and  spent  half  of  her  money; 

how  much  did  she  spend  ? 

12.  Henry  spent  four  cents  for  an  orange,  and  half  as 

much  for  an  apple;  how  much  did  both  cost? 
The  orange  cost  how  much  more  than  the  apple? 
18.  There  are  two  piles  of  boxes;  in  the  first  pile  there 
are  six  boxes;  in  the  second  pile  there  are  two- 
thirds  as  many.  How  many  boxes  are  there  in 
the  second  pile? 

*  In  all  such  problems  in  Part  First,  the  expression  "at  the  same  rate," 
or  its  equivalent,  is  understood. 


22  THE   RATIONAL   ARITHMETIC. 

1.  At  2  cents  eacli,  two  tops  will  cost cents. 

2.  Three  apples  and  two  apples  are apples. 

3.  A  nickel  equals  1  cent  and  two  times cents. 

4.  One-lialf  of  four  marbles  is marbles. 

5.  Tliree  pencils  at  1  cent  each,  and  one  pencil  at  2 

cents  together  will  cost cents. 

6.  A  rope  is  six  feet  long;  one -half  of  it  is 

feet  long. 

7.  At  2 J  cents  each,  two  blocks  of   paper  will   cost 

cents. 

8.  A  quart  of  milk  costs  6  cents,  and  one -third  of  a 

quart  costs cents. 

9.  When  peaches  cost  3  cents  each,  with  6  cents  one  can 

buy ^_  peaches. 

10.  One  quart  equals  two  pints,  and  two  quarts  equal 

pints. 

11.  Charlie  gave  one -half    of    an  apple  to  each  of  six 

boys,  to  all  he  gave apples. 

12.  A  boy  earned  6  cents  and  spent  4;    he  then  had 

cents  left. 

13.  A  man  walks  two  blocks  and  rides  three  more.     In 

all  he  goes blocks. 

14.  At  3  cents  each,  two  balls  will  cost cents. 

15.  Harry  had  six  marbles.     He  lost  three  and  bought 

one  more;  he  then  had marbles. 

16.  A  door  is  six  feet  high  and  two -thirds  as  wide.     Its 

width  is    feet. 

17.  Bessie  had  six  cents  and  spent  one-thi.id   of   her 

money.     She  then  had  cents. 

18.  When  oranges  are  2  cents  each,  for  9  cents  one  can 

buy ,  oranges. 


PART   FIRST. 


23 


Combinations  for  Drill: 
Addition 


2 

3 

1            2 

4 

3 

3 

2 

2 

5           4 

1 

3 

1 

2 

2 

1 

4 

2 

1 

1 

2 

3 

1 

2 

2 

1 

9 

1 

1 

1 

3 

1 

1 

3 

2 

1 

1 

1 

1 

1 

1 

4 

3 

1 

2 

1 

3 

1 

2 

1 

1 

1 

Subtraction 

4 

5 

4 

6 

5 

6 

2 

1 

3 

4 

3 

2 

6 

5 

6 

6 

5 

1 

2 

5 

3 

4 

Xof5 

;:;:: 

|of  6= 

4 

is  two 

times  ? 

fof  5 

■:zi 

|of  6- 

5 

is  two 

times  ? 

f  of  5 

= 

i  of  6- 

6 

is  two  times  ? 

A  of  5 

— 

|of6- 

6 

is  three  times  ? 

iof  6 

^zz 

i  of  6- 

6 

is  one 

and  one -half 

iof  6 

— 

fof  6- 

• 

times 

2 

• 

2isi 

of  ? 

3isi 

of  ? 

4  is  4  of  ? 

2isi 

of  ? 

3isi 

of  ? 

2i 

is  ^  of  ? 

2  isf 

of  ? 

4  isf 

of  ? 

5  is  1  of  ? 

24 


THE   RATIONAL   ARITHMETIC. 


1.  How  long  is  each  line? 

2.  How  long  are  the  green  line  and 

the  yellow  line  together  ?  The 
blue  and  the  orange  ?  The  pur- 
ple and  the  red? 

3.  How  long  are  the  green  line  and 

the  orange  line  together?  The 
blue  and  the  red?  The  purple 
and  the  red  and  the  yellow  ? 

4.  The  orange  line  and  which  line 

are  together  Y  inches  long? 

5.  The  red  line  and  which  line  are 

together  7  inches  long? 

6.  The  yellow  line  and  which  line 

are  together  7  inches  long? 

7.  The  orange  line  and  the  purple 

line  and  which  other  line  are 
together  7  inches  long? 

8.  Two  times  the  red  line  and  which 

other  line  are  together  7  inches 
long? 

9.  Two  times  the  yelloAV  line  and 

which  other  line  are  together 
7  inches  long? 

10.  Three  times  the  orange  line  and 

which  line  are  together  7  inches 
long? 

11.  The  orange  line  and  which  line 

are  together  8  inches  long  ? 

12.  The  red  line  and  which  line  ar^ 

together  8  inches  long? 


PART   FIRST.  25 

1.  Tlie  purple  line  and  the  red  line  and  whicli  other 

line  are  together  8  inches  long? 

2.  The  blue  line  and  the  yellow  line  and  which  other 

line  are  together  8  inches  long? 

3.  Two  times  the  orange  line  and  which  other  line  are 

together  8  inches  long? 

4.  Two  times  the  red  line  and  which  other  line  are 

together  8  inches  long? 

5.  Two  times  the  yellow  line  and  which  line  are  to- 

gether 8  inches  long? 

6.  If  from  a  line  equal  to  the  green  line  and  the  yellow 

line  we  take  a  line  equal  to  the  orange,  which 
line  will  the  remainder  equal  ? 

7.  If  from  a  line  equal  to  the  green  line  and  the  yellow 

line  we  take  a  line  equal  to  the  red,  w^hich  line 
mil  the  remainder  equal  ? 

8.  If  from  a  line  equal  to  the  green  line  and  the  orange 

line  we  take  a  line  equal  to  the  red,  which  line 
will  the  remainder  equal  ? 

9.  If  from  a  line  equal  to  the  green  line  and  the  orange 

line  we  take  a  line  equal  to  the  purple,  which 
line  will  the  remainder  equal  ? 

10.  Two  times  the  purple  line  equals  the  length  of  the 

green  line  and  which  other  line  together  ? 

11.  A  line  equal  to  the  green  line  and  the  orange  line 

together  is  two  times  as  long  as  which  line  ? 

12.  Four  times  the  orange  line  is  equal  to  a  line  made 

up  of  the  green  line  and  which  other  line  ? 

13.  A  line  equal  to  the  green  line  and  the  orange  line 

together  is  four  times  as  long   as  which   other 
line? 


26  THE   RATIONAL   ARITHMETIC. 

1.  7  inclies  equal  2  inches  and  3  inches  and 

inches. 

2.  7  inches  equal  4  inches  and  2  inches  and : 

inch. 

3.  7  inches  equal  1  inch  and  two  times inches. 

4.  8  inches  equal  2  inches  and  4  inches  and 

inches. 

5.  8  inches  equal  3  inches  and  2  inches  and 

inches. 

6.  8  inches  equal  2  inches  and  2  inches  and 

inches. 

7.  1  inch  is  what  part  of  7  inches?     2  inches  are  what 

part  ?     5  inches  are  what  part  ? 

8.  1  inch  is  what  part  of  8  inches?     3  inches  are  what 

part  ?     7  inches  are  what  part  ? 

9.  2  inches  are  what  part  of  8  inches? 

10.  6  inches  are  what  part  of  8  inches? 

11.  4  inches  are  what  part  of  8  inches? 

12.  7  inches  are  three  and  one -half  times inches. 

13.  2  inches  are  two -sevenths  of inches. 

14.  7  inches  are  two  times inches. 

15.  3^  inches  are  one -half  of inches. 

16.  7  inches  are  one  and  three -fourths  times 

inches. 

17.  4  inches  are  four-sevenths  of inches. 

18.  8  inches  are  four  times inches. 

19.  2  inches  are  one-fourth  of inches. 

20.  8  inches  are  two  times inches. 

21.  4  inches  are  one -half  of inches. 

22.  8  inches  are  one  and  one-third  times inches. 

23.  6  inches  are  three-fourths  of inches. 


.PART    FIRST.  27 

1.  Charle.s  had  4  picture  cards,  and  lils  mother  gave 

him  3  more;  how  many  had  he  then? 

2.  Mary  had  7  pigeons,  she  sold  2.     How  many  did 

she  have  left? 
8.  Clara  spent  2  weeks  in  the  country  at  Christmas, 
and  6  weeks  during  the  summer.      How  many 
weeks  did  she  spend  there  on  l)oth  visits  ? 

4.  Fred  is  8  years  old,  and  his  brother  is  half  as  old. 

How  old  is  his  brother  ? 

5.  A  boy  picked   8   quarts  of  berries,  and  sold  6  of 

them.     How  many  quarts  had  he  left  ? 

6.  Robert  had  7  cents.     He  bought  as  many  balls  at 

3  cents  each  as  he  could.  How  many  did  he  get^ 
and  how  many  cents  did  he  have  left?  A¥hat 
part  of  his  money  was  left  ? 

7.  If  one  orange  costs  4  cents,  how  much  will  2  oranges 

cost  ? 

8.  James  earned  8  cents,  and  spent  J  of  it.     How  much 

money  did  he  have  left  ? 

9.  A  girl  was  sick  two  days  in  one  week.     What  part 

of  the  seven  days  ^vas  she  sick  ? 

10.  Alice  had  8  flowers.      She  gave  6  to  her  teacher. 

What  part  did  she  give  her  ? 

11.  A  boy  had  8   cents,  and  paid   2  cents  for  a  ball. 

What  part  of  his  money  did  he  spend  for  the  ball  ? 

12.  Frank  spent  7  cents  for  candy,  and  May  spent  y  as 

much.  How  much  did  May  spend?  How  much 
did  both  spend  ? 

13.  Julia's  book  is  8  inches  long  and  h  as  wide.     How 

wide  is  it?     It  is  ^  as  thick  as  it  is  wide.     How 
kisit?-'    •■  '    •-•■-- 


28 


THE   RATIONAL  ARITHMETIC. 


i 


i 


I 


I 


1.  Find  the  lengtli  of  every  line. 

2.  How  long  are  the  green,  the  orange, 

and  the  yellow  line  together  ? 

3.  How  long  are  the  blue  and  the 

purple  line  together? 

4.  How  long  are  the  green  and  the 

red  line  together  ? 

5.  The  green  line  is  equal  to  how 

many  lines  the  length   of  the 
red? 

6.  How  many  lines  the  length  of  the 

red  can  be  made  from  one  9 
inches  long? 

7.  How  long  are  the  green,  the  red, 

and  the  yellow  line  together  ? 

8.  How  long  are  the  blue,  the  orange, 

and  the  red  line  together  ? 

9.  How  long  are  the  blue,  the  purple, 

and  the  yellow  line  together  ? 

10.  How  long  are  the  green  and  the 

purple  line  together? 

11.  How  long  are  the  green  and  the 

blue  line  together  ? 

12.  How  long  are  the  yellow,  the  green, 

and  the  purple  line  together  ? 

13.  How  long  are  the  orang  , the  green, 

and  the  red  line  together  ? 

14.  How  long  are  the  purple,  the  blue, 

and  the  orange  line  together  ? 

15.  The  green  line  and  which  line  are 

toQfether  9  inches  Ions:? 


PART   FIRST.  29 

1.  The  blue  line  and  which  line  are  together  9  inches 

long  ? 

2.  The  purple  line  and  the  orange  line  and  which  other 

line  are  together  9  inches  long? 

3.  The  red  line  and  which  line  are  together  9  inches 

long? 

4.  Two  times 'the  purple  line  and  which  line  are  together 

9  inches  long? 

5.  Two  times  the  red  line  and  which  two  lines  are  to- 

gether 9  inches  long? 

6.  Which  two  lines  are  together  9  inches  long? 

7.  The  blue,  the  red,  and  which  line  are  together  10 

inches  long? 

8.  The  green,  the  red,  and  which  line  are  together  10 

inches  long? 

9.  The  ]3urple  line  and  which  line  are  together   10 

inches  Ions;? 

10.  Two  times  the  pur]3le  line  and  which  line  are  to- 

gether 10  inches  long? 

11.  Three  times  the  orange  line  and  which  line  are  to- 

gether 10  inches  long? 

12.  Two  times  which  line  equals  10  inches? 

13.  The  green,  the  purple,  and  which  line  are  together 

11  inches  long? 

14.  The  blue,  the  orange,  and  which  line  are  together 

11  inches  long? 

15.  The  green,  the  orange,  and  which  line  are  together 

11  inches  long? 

16.  Which  two  lines  are  together  11  inches  long? 

17.  Two  times  the  purple  line  and  which  line  are  to- 

■  gether  11  inches  long?  •      ^ 


30  THE   RATIONAL  ARITHMETIC. 

1.  Two  times  tlie  blue  line  and  whicli  line  are  together 

11  inches  long? 

2.  If  from  a  line  as  long  as  the  green  and  the  red 

together,  we  take  a  line  equal  to  the  blue,  which 
line  will  the  remainder  equal  ? 

3.  If  from  a  line  as  long  as  the  green  and  the  red  to- 

gether, we  take  a  line  equal  to  the  purple,  which 
line  will  the  remainder  equal? 

4.  If  from  a  line  as  long  as  the  green  and  the  purple 

together,  we  take  a  line  equal  to  the  blue,  which 
line  will  the  remainder  equal  ? 

5.  If  from  a  line  as  long  as  the  green  and  the  blue  to- 

gether, we  take  a  line  equal  to  the  orange,  which 
lines  will  the  remainder  equal  ? 

6.  If  from  a  line  as  long  as  the  green  and  the  blue  to- 

gether, we  take  a  line  equal  to  the  yellow,  ^vhich 
lines  vnll  the  remainder  equal  ? 

7.  How  long  are  the  red   line  and   the  orange   line 

together  ? 

8.  How  long  are  the  blue,  the  red,  and  the  orange  line 

together  ? 

9.  How  many  lines  the  length  of  the  blue  can  be  made 

from  the  blue,  the  red,  and  the  orange  line  together  ? 

10.  The  blue  line  is  what  part  of  a  line  10  inches  long? 

11.  How  many  inches  long  is  a  line  which  is  one -half  of 

a  line  10  inches  long? 

12.  The  blue  and  the  red  line  together  are  how  many 

times  as  long  as  the  orange  ? 
18.  The  orange  line  is  what  part  of  a  line  10  inches  long? 

14.  The  purple  line  is  what  part  of  a  line  10  inches  long  ? 

15.  The  green  line  is  what  part  of  a  line  10  inches  long? 


PART   FIRST.  31 


1.  9  inclies  are  3   inclies   and  4  inclies  and 

inclies. 

2.  9  inclies  are   2  inclies  and  3  inclies  and 

inclies. 

3.  9  inches  are  3  inches  and  3  inches  and 

inches. 

4.  10  inches  are  5  inches  and  3  inches  and 

inches. 


5.  10  inches  are  4  inches  and  5  inches  and inch. 

6.  10  inches  are  3  inches  and  2  inches  and 

inches. 

7.  10  inches  are  5  inches  and  2  inches  and 

inches. 

8.  11  inches  are  8  inches  and inches. 

9.  11  inches  are  4  inches  and  . inches. 

10.  11  inches  are  6  inches  and  . inches. 

11.  11  inches  are  5  inches  and  3  inches  and . 

inches. 

12.  11  inches  are  7  inches  and  2  inches  and 

inches. 

13.  What  part  of   9   inches  is   1  inch?      Two  inches? 

Four  inches  ?    Five  inches  ?    Seven  inches  ?    Eight 
inches  ? 

14.  What  j)art  of  9  inches  are  3  inches  ?     6  inches  ? 

15.  What  j)art  of  9  inches  are  4^  inches? 

16.  9  inches  are  how  many  times  1  inch?     2  inches?     4 

inches?     5  inches?     7  inches?     8  inches? 

17.  9  inches  are  how  many  times  3  inches?     6  inches? 

4 J  inches? 

18.  What  part  of  10  inches  is   1   inch?     3  inches?     7 

inches?     9  inches? 


THE   RATIONAL  ARITHMETIC. 


1. 

2. 
3. 

4. 

5. 
6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 

19. 
20. 

21. 
22. 
23. 
24. 


What  part  of  10  inches  are  2  inches?     4  inches?     6 

inches?     8  inches? 
What  part  of  10  inches  are  5  inches? 
10  inches  are  how  many  times  1  inch?     3  inches? 

7  inches?     9  inches? 
10  inches  are  how  many  times  2  inches?     4  inches? 

6  inches?     8  inches? 

10  inches  are  how  many  times  5  inches? 

What  part  of  11  inches  is  1  inch?     2  inches?     3 
inches  ? 

11  inches  are  how  many  times  I   inch?     2  inches? 
3  inches? 

9  inches  are  three  times inches. 

3  inches  are  one -third  of inches. 


9  inches  are  one  and  one-half  times 

6  inches  are  two -thirds  of inches. 

9  inches  are  two  times inches. 


inches. 


4  J  inches  are  one -half  of 
10  inches  are  five  times  _ 
2  inches  are  one -fifth  of  _ 


_  inches. 

inches. 

inches. 


10  inches  are  two  and  one -half  times 

4  inches  are  two -fifths  of inches. 

10  inches  are  one  and   two -thirds  times  _ 

inches. 

6  inches  are  three -fifths  of inches. 

10  inches  are  one  and   one -fourth  times  _ 

inches. 

8  inches  are  four -fifths  of inches. 

10  inches  are  two  times inches. 

5  inches  are  one -half  of inches. 


inches. 


51  inches  are  one -half  of 


inches. 


PART   FIRST.  33 

1.  James  rode  six  miles  on  his  bicycle  one  day,  and 

three  miles  the  next  day.     How  many  miles  did 
he  ride  in  both  days? 

2.  A  child  goes  to  school  five  days  each  week.     How 

many  days  does  he  go  to  school  in  two  weeks  ? 

3.  A  boy  earned  10  cents.     He  lost  1  cent,  and  spent 

one-third  of  the  remainder.     How  much  did  he 
have  left? 

4.  How  may  eleven  apples  be  divided  equally  between 

two  boys? 

5.  How  many  pieces  of  wood  two  feet  long  can  be 

sawed  from  a  board  ten  feet  long? 

6.  A  table  is  three  feet  wide,  and  three  times  as  long. 

How  long  is  it? 

7.  A  boy  had  ten  papers  and  sold  all  but  one -fifth  of 

them.     How  many  had  he  left? 

8.  At  2  cents  each,  how  much  will  five  pencils  cost? 

9.  A  rug  is  eight  feet  wide,  and  two  feet  longer  than 

wide.     How  long  is  it  ? 

10.  There  are  nine  seats  in  one  row,  and  two -thirds  as 

many  in  the  next.     How  many  seats  are  there  in 
the  second  row? 

11.  A  pile  of  stone  is  nine  feet  long  and  two-thirds  as 

wide.     How  wide  is  it?     It  is  one-half  as  high  as 
it  is  wide.     How  high  is  it  ? 

12.  A  street  car  goes  six  miles  an  hour.     How  many 

miles  will  it  go  in  one  and  one-half  hours?    In 
one  and  one-third  hours? 

13.  One  jug  holds  four  quarts.     How  many  such  jugs 

can  be  filled  from  nine  quarts  ?   How  many  quarts 
mil  be  left? 


34  THE   RATIONAL   ARITHMETIC. 

1.  If  one  bin  holds  three  bushels,  how  many  bushels 

will  two  such  bins  hold  ?  How  many  such  bins 
will  be  required  to  hold  nine  bushels  ?  How  many 
will  be  required  to  hold  eleven  bushels  ? 

2.  A  cistern  ten  feet  deep  is  half  full  of  water.     How 

many  feet  of  water  are  there  in  it  ? 
\  Four  quarts  equal  one  gallon.     How  many  gallons 
do  ten  quarts  equal  ?     Eleven  quarts  ? 

4.  A  rope  is  nine  feet  long;  one -third  of  it  is  cut  off. 

What  j)art  remains,  and  what  is  its  length  ? 

5.  A  set  of  six  books  costs  9  dollars.     What  will  one 

of  these  books  cost  ?     Three  ? 

6.  A  box  is  eleven  inches  long,  six  inches  wide  and 

three  inches  high.  How  much  longer  is  it  than 
it  is  wide?  How  much  longer  is  it  than  it  is 
high  ?     How  much  wider  is  it  than  it  is  high  ? 

7.  There  are  eleven  cars  in  one  train;  nine -elevenths  as 

many  in  the  second;  and  seven-elevenths  as  many 
in  the  third.  How  many  cars  are  there  in  the 
second  train  ?     The  third  train  ? 

8.  A  wire  ten  feet  long  is  cut  into  three  equal  parts. 

How  long  is  each  part  ?  How  long  would  each 
part  be  if  the  wire  were  cut  into  four  equal  parts  ? 
Into  five  equal  parts?     Into  six  equal  parts? 

9.  One  panel  of  a  door  is  three-fourths  of  a  foot  wide; 

how  wide  are  two  such  panels  ?  The  door  is  twice 
as  wide  as  two  panels;  how  wide  is  the  door? 
10.  How  many  pieces  of  paper  one  inch  wide  and  three 
inches  long  can  be  cut  from  a  strip  one  inch  wide 
and  nine  inches  long?  From  a  piece  two  inches 
wide  and  nine  inches  long  ? 


PART   FIRST. 


35 


Combinations  for  Drill: 
Addition 


5 

3 

3 

6 

4 

D 

7 

6 

2 

4 

5 

9 

4 

4 

0 

3 

7 

6 

8 

5 

6 

4 

8 

2 

3 

4 

2  ■ 

5 

5 

7 

3 

9 

3 

4 

1 

2 

3 

2 

4 

3 

2 

3 

5 

3 

3 

3 

0 

4 

2 

1 

2 

4 

3 

0 

2 

4 

Subtraction 

7 

8 

9 

10 

11 

7 

8 

9 

4 

4 

3 

6 

5 

0 

2 

5 

10 

11 

8 

10 

11 

9 

11       : 

LI 

5 

7 

5 

8 

3 

2 

6 

9 

1 

7 

of  7 

i  of  8: 

^z 

iof  9  = 

I 

i  of  10 

— 

5 

T 

of  7 

iof  8 

= 

f  of  9  = 

= 

-1  of  10 

— 

1 
8 

of  8- 

i  of  8 

nn 

1  of  9  = 

: 

lof  10 

4 

= 

f 

of  8- 

i  of  9: 

I^ 

iVof  10 

TVofll 

— 

1 

of  8  = 

4   of   9: 

:::; 

-r^o  of  10 

— 

A  of  11 

— 

7  is  two  times  ? 

8  is  two  times  ? 
8  is  four  times  ? 


9  is  three  times  ? 
10  is  two  times  ? 
10  is  ^ve  times  ? 


2  is  i  of  ?      3  is  i  of  ?       5  is  1  of  ? 
?      4  is  I  of  ?       5  is  I  of  ? 


6  is  f  of 


2  is  -^  of 


8is|- 


7 
of  ? 


36 


THE  RATIONAL  ARITHMETIC. 


1.  How  many  inches   long   are 

tlie  green  and  tlie  black  line 
together  ? 

2.  What   do   we   call    so    many 

inches  ? 

3.  How  many  times   the   green 

line  equal  a  foot?  The 
green  line  equals  what  part 
of  a  foot? 

4.  How  many  times   the   black 

line  equal  a  foot?  The 
black  line  equals  what  part 
of  a  foot? 

5.  The  green,  the  blue,  and  which 

other  line  equal  a  foot  ? 

6.  The  red,  the  purple,  and  which 

other  line  equal  a  foot  ? 

7.  The  red,  the  yellow,  the  orange, 

and  which  other  line  equal 
a  foot? 

8.  How  many  times  the  red  line 

equal  a  foot  ?  The  red  line 
equals  what  part  of  a  foot  ? 

9.  How  many  times  the  red  line 

equal  three -fourths  of  a  foot  ? 
How  many  inches  equal 
three -fourths  of  a  foot? 
10.  How  many  times  the  purple 
line  equal  a  foot  ?  The  pur- 
ple line  equals  what  part  of 
a  foot? 


PART   FIRST.  37 

1.  How  many  times  the  purple  line  equal  two -thirds 

of  a  foot?  How  many  inches  equal  two -thirds  of 
a  foot? 

2.  How  many  times  the  orange  line  equal  a  foot?    The 

orange  line  equals  what  part  of  a  foot  ? 

3.  How  many  times  the  orange  line  equal  one -half  of 

a  foot  ?  How  many  times  the  orange  line  equal 
two -sixths  of  a  foot?  How  many  equal  three - 
sixths?     Four-sixths?     Five-sixths? 

4.  Which  two  lines  together  equal  one -half  of  a  foot? 

Two-halves  of  a  foot?  One-quarter  of  a  foot? 
Three-quarters  of  a  foot?  One-third  of  afoot? 
Two -thirds  of  a  foot? 

5.  How  many  inches  are  there  in  one -sixth  of  a  foot? 

In  two -sixths?     In  three -sixths?     In  four -sixths? 

6.  How  many  6  inches  are  there  in  1  foot? 

7.  How  many  3  inches  are  there  in  1  foot? 

8.  How  many  4  inches  are  there  in  1  foot? 

9.  How  many  2  inches  are  there  in  1  foot? 

10.  Twelve  are  two 

11.  Twelve  are  four . 

12.  Twelve  are  three 

13.  Twelve  are  six . 


14.  Twelve  are  twelve 

15.  One  foot  is inches. 

16.  One -half  of  a  foot  is inches. 

17.  One-fourth  of  a  foot  is inches. 

18.  Two -halves  of  a  foot  are inches. 

19.  Two -fourths  of  a  foot  are inches. 

20.  Three -fourths  of  a  foot  are inches. 

21.  Four-fourths  of  a  foot  are inches. 


38 


THE   RATIONAL   ARITHMETIC. 


1. 

2. 
3. 
4. 

D. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 


6  inches  are  one -half  of 

3  inclies  are  one- fourth  of 

6  inclies  are  two -fourths  of  _ 
9  inches  are  three -fourths  of 

One -third  of  a  foot  is 

One -sixth  of  a  foot  is 

Two -sixths  of  a  foot  are 

Two -thirds  of  a  foot  are 

Three -sixths  of  a  foot  are 

Three -thirds  of  a  foot  are 

Four -sixths  of  a  foot  are 

Five -sixths  of  a  foot  are 

Six -sixths  of  a  foot  are 

4  inches  are  one -third  of 

8  inches  are  two -thirds  of 

2  inches  are  one -sixth  of 

4  inches  are  two -sixths  of 


inches. 

inches. 

inches. 

inches. 


inches, 
inches. 

inches. 

inches. 

inches. 

inches. 

inches. 

inches. 

_  inches. 

inches. 

inches. 

inches. 

inches. 


Draw  a  line  one -half  of  a  foot  long. 
Draw  a  line  one -fourth  of  a  foot  long. 
Draw  a  line  one -third  of  a  foot  long. 
Draw  a  line  one -sixth  of  a  foot  long. 
Draw  a  line  one -twelfth  of  a  foot  long. 
Draw  a  line  two -fourths  of  a  foot  long. 
Draw  a  line  two -thirds  of  a  foot  long. 
Draw  a  line  two -sixths  of  a  foot  long. 
Draw  a  line  two -twelfths  of  a  foot  long. 
Draw  a  line  three -fourths  of  a  foot  long. 
Draw  a  line  three -sixths  of  a  foot  long. 
Draw  a  line  three -twelfths  of  a  foot  long. 
Draw  a  line  four -sixths  of  a  foot  long. 
Draw  a  line  four -twelfths  of  a  foot  long. 


PART  FIRST.  39 

1.  What  are  twelve  inches  called  ? 

2  What  is  the  same  number  of  eggs  called  ? 

3  What  is  the  same  number  of  months  called  ? 

4.  How  many  winter  months  are  there  ?    What  part  of 

a  year  are  the  winter  months  ? 

5.  How  many  summer  months  are  there?     What  part 

of  the  year  are  the  summer  months  ? 

6.  What  part  of  the  year  are  the  winter  and  summer 

months  together  ? 

7.  How  many  spring  months  are  there?     How  many 

fall  months  are  there  ? 

8.  Each  season  is  what  part  of  a  year?     Each  month 

is  what  part  of  a  year  ? 

9.  If  eggs  are  12  cents  a  dozen,  what  will  three-fourths 

of  a  dozen  cost?     Two-thirds  of  a  dozen?     One- 
half  of  a  dozen  ? 

10.  If  ten  peaches  cost  12  cents,  how  much  will  ^ve 

peaches  cost? 

11.  Eight  lemons  cost  8  cents;  how  much  will  a  dozen 

cost  ? 

12.  Tom  has  twelve  marbles,  and  George  has  two -thirds 

as  many  ?     How  many  marbles  has  George  ? 

13.  Harry  spent  9   cents,  which  was  three -fourths  of 

what  he  earned;  how  much  did  he  earn? 

14.  A  rectangular  flowxr  bed  is  four  feet  long  and  two 

feet  wide.     What  is  the  distance  around  the  bed? 

15.  How  many  inches  are  there  in  the  perimeter"^  of  a 

square  whose  side  measures  three  inches  ? 

16.  How  many  feet  are  there  in  the  perimeter  of  a  rug 

that  is  three  feet  long  and  two  feet  wide  ? 

*  The  "  perimeter  "  is  the  distance  around. 


40  THE   RATIONAL   ARITHMETIC. 

1.  George  had  12  cents  and  paid  one -fourth  of  it  for  a 

ruler.  How  much  did  he  pay  for  the  ruler? 
What  part  of  12  cents  would  he  have  paid  for 
three  rulers? 

2.  If  a  man  can  do  a  piece  of  work  in  twelve  days, 

what  part  of  it  can  he  do  in  four  days  ?  In  eight 
days  ? 

3.  If  strawberries  sell  for  12  cents  a  box,  and  currants 

for  five -sixths  as  much,  how  much  will  a  box  of 
currants  sell  for? 

4.  John  walked   twelve   miles  in  a  day,  and   George 

walked  three -fourths  as  far.  How  far  did  George 
walk? 

5.  A  man  earns  2  dollars  a  day.     How  long  will  it  take 

him  to  earn  12  dollars? 

6.  How  many  2 -cent  postage  stamps  can  be  bought  for 

a  dime  and  2  cents  ? 

7.  Harry  found  six  eggs  in  one  nest  and  two  in  another. 

What  part  of  a  dozen  did  he  find  ? 

8.  If  eight  apples  are  worth  6  cents,  how  much  is  a 

dozen  worth  ? 

9.  If  one  reads  a  book  every  month,  how  many  books 

will  he  read  in  three -fourths  of  a  year?  How 
many  in  two -thirds  of  a  year? 

10.  A  shepherd  had  eight  lambs  in  a  pen.     This  was 

two -thirds  as  many  as  he  had  in  another  pen. 
How  many  did  he  have  in  the  second  pen  ? 

11.  There  are  twelve  chickens  in  a  coop;  five -sixths  as 

many  in  the  yard;  two -thirds  as  many  in  the  barn, 
and  three -fourths  as  many  in  a  vacant  lot.  How 
many  are  there  in  each  place  ? 


PART  FIRST. 


41 


Combinations  for  Drill: 
Addition 

8  11 

4  1 


9 
3 


6 
6 


10 

2 


0 


6 

3 

6 

2 

4 

2 

2 

2 

3 

4 

4 

8 

4 

7 

3 

6 

4 

2 

4 

5 

6 

2 

3 

1 

7 

• 

12 

• 

12 

• 

12 

2 

• 

12 

7 

• 

12 

1 

• 

12 

Subtraction 

12 

12 

12 

12 

12 

12 

8 

3 

6 

4 

9 

5 

12 

12 

12 

12 

12 

12 

2 

• 

2 

• 

? 

2 

• 

? 

2 

• 

11 


10 


8 


iof  8- 
i  of  10= 
i  of  12= 
iof  6= 


JL 

3 

JL 

3 

2 
S 

2 
If 

3 


of  9= 
of  12  = 
of  6= 
of  9= 
of  12= 


iof  8= 


1 


1  of  12 


I  of  12: 
^of  8= 


3 


^   of   12: 


12  is  two  times  ?      12  is  six  times  ? 

12  is  three  times  ?     12  is  one  and  one -half  times  ? 

12  is  four  times  ?     12  is  one  and  one -third  times  ? 


2  is  -J-  of 

3  is  i  of 


4  is 

6  18 


2 


iof 
*of  ? 


8  is  f  of  ? 

9  is  f  of  ? 


42 


THE    RATIONAL  ARITHMETIC. 


Ones 

Zero 

0 

ITen 
Ten 

Ten 

0 

2Tei8 
Twenty 

3  Tens 
Thirty 

30 

3 

32 

33 

34 

35 

3I0 

3^ 

38 

3c 

4  Tens 
Forty 

40 
14 

42 

43 

44 

45 

4b 
14 -- 

48 
14c 

5  Tens 
Fifty 

50 
5 

5  9. 
53 

6  Tens 
Sixty 

bo 

Q 

b9. 
o3 

7  Tens 
Seventy 

qo 

n 

q2 
^3 
■14 
^5 

nc 

8  Tens 
Eighty 

80 

8 

82 

83 

84 

85 

Sb 

8-^ 

88 

8c 

9  Tens 

Ninety 

a 
V' 

c|4 

^5 

cjlo 
or 

c]8 
ac 

10  Tens 
On«  Hnndred 

Twenty 

'?-0 

00 

One 

Two 

Three 

3 

Four 
Lj. 

Five 

5 

Six 

b 

Seven 

n 

Eight 

8 

Nine 
C 

Eleven 

Twelve 
12 

Thirteen 

3 

Fourteen 
14 

Fifteen 

5 

Sixteen 

b 

Seventeen 
r- 

Eighteen 

8 

Nineteen 
C 

Twenty-One 

2 

Twenty-Two 

Twenty-Three 

23 

Twenty-Four 

9.4 

54 
55 
5I0 
5^ 
58 
5C 

b4 
b5 
bb 
b"j 
bS 
be 

Twenty-Five 

25 

Twenty-Six 

Twenty -Seven 

9.q 

Twenty- Eight 

7,8 

Twenty-Nine 

2c 

Read  across  the  page  — 10,  20,  30,  etc.;  1, 11,  21,  31,  etc. 

Read  downward  by  columns — 1,  2,  3,  etc.;  10, 11, 12,  etc. 

Draw  similar  diagrams,  and  fill  in,  commencing  with  100,  200,  etc. 


PART   FIRST. 


43 


9 

4 

2 

6 

( 

7 

8 

5 

3 

8 

18 

28 

38 

1 

48 

58 

68 

78 

4 

14 

24 

34 

4 

44 

54 

64 

74 

3 

8 

5 

2 

2 

4 

7 

6 

9 

7 

17 

11 

37 

2 

Al 

V 

67 

77 

3 

13 

23 

35 

4 

43 

53 

63 

75 

8 

6 

4 

3 

3 

2 

5 

7 

9 

5 

15 

25 

55 

2 

45 

55 

65 

75 

3 

13 

23 

33 

5 

43 

53 

65 

73 

5 

3 

8 

7 

4 

6 

2 

4 

9 

6 

16 

26 

36 

3 

46 

56 

66 

76 

2 

12 

?? 

32 

6 

42 

52 

62 

71 

Add  the  red  figure  to  each  black  figure  in  the  same  large  square. 
Take  the  red  figure  from  each  equal  or  larger  black  figure  in  the  same 
large  square. 

The  above  arrangement  supplies  material  for  still  other  drill  work. 


1 

1 

1 

2 

1 

2 

1 

2 

3 

1 

2 

1 

2 

3 

2 

4 

3 

5 

4 

3 

6 

5 

3 

1 

2 

8 

4 

1 

2 

3 

4 

1 

2 

4 

7 

6 

5 

4 

8 

7 

6 

5 

9 

8 

3 

4 

5 

2 

3 

4 

5 

3 

4 

5 

6 

7 

6 

5 

9 

8 

7 

6 

9 

8 

7 

6 

The  above  fundamental  combinations  should  become  automatic. 


u 


THE  RATIONAL  ARITHMETIC. 


m  »  «ifaiairf. 


1.  What  is  the  size  of  the  yellow  square? 

2.  How  long  is  the  green  rectangle?     How  wide  is  it? 

3.  How  many  square  inches  are  there  in  the  rectangle? 


PART   FIRST.  45 

1.  1  square  inch  is  what  part  of  its  surface,  or  area? 

2.  How  long  are  the  sides  of  the  purple  square? 

3.  How  many  rows  of  square  inches  are  there  in  the 

purple  square? 

4.  How  many  square  inches  are  there  in  the  upper  row 

of  the  purple  square  ?     How  many  square  inches 
are  there  in  the  whole  square  ? 

5.  One  row  is  what  part  of  its  area? 

6.  1  square  inch  is  what  part  of  one  row? 

7.  1  square  inch  is  what  part  of  its  whole  area?     2 

square  inches  are  what  part  ? 

8.  How  long  and  how  wide  is  the  blue  rectangle  ?    Or, 

what  are  the  dimensions  of  the  blue  rectangle  ? 

9.  How  many  square  inches  are  there  in  the  blue  rect- 

angle ? 

10.  1  square  inch  is  what  part  of  its  area?     2  square 

inches  are  what  part  ? 

11.  What  are  the  dimensions  of  the  orange  rectangle? 

12.  How  many  square  inches  are  there  in   the  orange 

rectangle  ? 

13.  What  are  the  dimensions  of  the  red  rectangle? 

14.  How  many  rows  of  3  square  inches  are  there  in  the 
red  rectangle  ? 

15.  How  many  square  inches  are  there  in  the  red  rect- 
angle ? 

16.  1  square  inch  is  what  part  of  the  area  of  the  red 
rectangle  ?     2  square  inches  are  what  part  ? 

17.  How  many  rows  of  2  square  inches  are  there  in  the 
red  rectangle  ? 

18.  One  row  is  what  part  of  the  area? 

19.  One-third  equals  how  many  sixths? 


46 


THE   RATIONAL   ARITHMETIC. 


1 .  How  long  is  tlie  red  rectangle  ?     How  wide  is  it  ? 

2.  How  many  rows  of  4  square  inches  are  there  in  the 

red  rectangle  ? 
8.  One  row  is  what  part  of  its  area? 
4.  How  many  rows  of  2  square  inches  are  there? 


PART   FIRST.  47 

1.  What  part  of  its   area  is   one   row?      Two  rows? 

Three  rows? 

2.  How  many  square  inches  are  there  in  the  rectangle? 

3.  How  many  2  square  inches  are  there  in  the  surface? 

How  many  3  square  inches  ?    How  many  4  square 
inches  ? 

4.  What  are  the  dimensions  of  the  ]>lue  rectangle  ? 

5.  How  many  rows  of  5  square  inches  are  there  in  the 

rectangle  ?     One  row  is  what  part  of  its  area  ? 
0.  How  many  square  inches  are  there  in  its  surface? 

7.  How  many  rows  of  2  square  inches  are  there  in  the 

surface  ? 

8.  What  part  of  its  area  is   one   row?      Two   rows? 

Three  rows  ?     Four  rows  ? 

9.  What  part  of  its  area  is  1  square  inch?     2  square 

inches?     3  square  inches?     4  square  inches? 

10.  The  area  of  the  red  rectangle  equals  what  part  of 

the  area  of  the  blue  rectangle  ? 

11.  How  many  two -inch  squares  can  be  made  from  the 

red  rectangle  ?     From  the  blue  rectangle  ? 

12.  How  many  rectangles  3  inches  long  and  1  inch  wide 

can  be  made  from  the  red  rectangle  ?     From  the 
blue  rectangle? 

13.  How  many  square  inches  are  there  in  a  two -inch 

square  ? 

14.  What  are  the  dimensions  of  a  rectangle  having  the 

same  area  as  a  two -inch  square? 

15.  What  is  the  length  of  the  perimeter  of  a  one -inch 

square?     Of  a  two -inch  square?    Of  the  red  rect- 
angle ? 

16.  Draw  rectangles  containing  6  square  inches. 


48 


THE   RATIONAL   ARITHMETIC. 


1.  How   long   and   how 

wide  is  tlie  orange 
rectangle  ? 

2.  What  is  its  area? 

3.  How  many  rows  of  6 

square  inches  are 
there  in  the  rect- 
angle ? 

4.  One  row  is  what  j)art 

of  the  rectangle  ? 

5.  How    many   rows   of 

2  square  inches  are 
there  ? 

6.  What  part  of  the  area 

is  one  row?  Two 
rows  ?  Three  rows  ? 
Four  rows?  Five 
rows  ? 

7.  How  many   two -inch 

squares  can  be  made 
from  the  rectangle  ? 

8.  How  many  rectangles 

3  inches  long  ahd  2 
inches  wide  caii  l)e 
made  ?  How  nkany 
rectangles  3  inches 
long  and  1  Inch 
wide  ? 

9.  Draw    other    rectan- 

gles containing  12 
square  inches. 


PART   FIRST.  49 

1.  In  tlie  preceding  figures,  find  the  one  tliat  shows  two 

ones;  the  figure  that  shows  two  twos;  two  threes; 
two  fours;  two  fives;  tAVo  sixes. 

2.  HoAV  many  2^s  in  2  ?  How  many  2's  in  8  ? 

How  many  2's  in  4?         How  many  2's  in  10? 
How  many  2's  in  6?         How  many  2's  in  12? 

3.  One  side  of  a  square  piece  of  glass  is  two  inches 

long.     How  many  square  inches  does  it  contain  ? 

4.  How  many  square  rods  are  there  in  a  field  that  is 

three  rods  long  and  two  rods  wide  ? 

5.  The  top  of  a  desk  contains  six  square  feet,  and  is 

three  feet  long.     How  ^vide  is  it  ? 

6.  There  are  eight  square  feet  in  a  window  that  is  four 

feet  high.     How  ^nde  is  it? 

7.  How  many  square  yards  of  carpet  are  there  in  a 

piece  one  yard  wide  and  four  }'ards  long  ?     In  a 
piece  two  yards  wide  and  four  yards  long  ? 

8.  A  sidewalk  is  two  feet  mde.    How  long  will  a  part 

of  it  be  that  contains  twelve  square  feet  ? 

9.  How  many  square  feet  are  there  in  one  side  of  a 

board  that  is  two  feet  long  and  one  foot  wide? 
How  many  square  feet  are  there  in  both  sides  ? 

10.  A  table  is  two  feet  wide  and  three  times  as  long. 

What  is  its  length  ?     How  many  square  feet  does 
it  contain  ? 

11.  A  piece  of  land  is  three  rods  long  and  one  rod  wide. 

How  many  rods    of   fence   will    be    required   to 
inclose  it? 

12.  A  field  is  four  rods  long  and  two  rods  wide.     What 

is  the  length  of  all  of  its  sides?      What  is  its 
area  ? 


50 


THE   RATIONAL   ARITHMETIC. 


) 

^r 


ftfii- 


PART   FIRST.  51 

1.  What  do  we  call  the  yellow  figure?     What  is  its 

area  ? 

2.  What  part  of  its  surface  is  one  row?     Two  rows? 

3.  AVhat  part  of  its  surface  is  1  square  inch?     2  square 

inches?     4  square  inches?     3  square  inches? 

4.  How  many  two -inch  squares  can  he  cut  from  the 

yellow  square  ?     How  many  can  be  made  from  it  ? 
Draw  a  square  and  illustrate. 

5.  What  are  the  dimensions  of  the  green  rectangle? 

0.  How  many  two-inch  squares  can  be  cut  from  it? 
How  many  can  be  made  from  it  ?  DraAV  a  square 
and  illustrate.  •     ^ 

7.  How  many  three -inch  squares  can  be  made  from  it? 

8.  How  many  rectangles  containing    2    square  inches 

can  be  made  from  it?     How  many  containing  3 
square  inches  ?    4  square  inches  ?    6  square  inches  ? 

9.  Draw: 

A  square  containing  4  square  inches.     What  are 

its  dimensions? 
A  rectangle  containing  4  square  inches.      What 

are  its  dimensions? 
A  square  containing  9  square  inches.     What  are 

its  dimensions? 
A  rectangle  containing  9  square  inches.     What 

are  its  dimensions? 
A  rectangle  containing  8  square  inches.     What 

are  its  dimensions? 
A  rectangle  containing  10  square  inches.     What 

are  its  dimensions  ? 
A  rectangle  containing  12  square  inches.     What 

are  its  dimensions? 


6^ 


THE   RATIONAL  ARITHMETIC. 


1.  What  are  tlie  dimensions  of  tlie  blue  rectangle? 

2.  What  is  its  area? 

3.  What  squares  and  rectangles  can  be  cut  or  made 

from  it  ? 


PART   FIRST. 


53 


1.  What  is  the  largest  square  tliat  can  be  cut  from  tlie 

blue  rectangle  ? 

2.  How  many  rows  of  3  square  inches  are  there  in  the 

blue  rectangle? 

3.  How  many  rows  of  5  square  inches  are  there? 

4.  What  part  of  the  area  is  3  square  inches?     6  square 

inches?     9  square  inches?     12  square  inches? 

5.  What  part   of   the   area  is   5   square  inches?      10 

square  inches? 

6.  What  is  the  length  of  the  perimeter  of  the  blue 

rectangle  ? 

7.  Draw  another  rectangle  whose    area   is    15  square 

inches. 

8.  6  and  6  are 

9  and  3  are 

8  and  4  are 

10  and  2  are 

7  and  5  are 

9.  12  less  3  is 

12  less  6  is 

12  less  9  is 

12  less  4  is 

12  less  8  is 


12  and  3  are 


fi  anrl  9  are 

.5  anrl  10  are 

8  and  7  are 

• 

11   and  4  are 

1.^  less  .5  is 

. • 

15  less  3  is 

15  less  10  is 

• 

15  less  9  is 

15  less  12  is 

10.  What  part  of  12  is  3? 
AVhatpart  of  12  is  4? 
What  part  of  12  is  9? 
What  jiart  of  12  is  6? 
What  fjart  of  12  is  8? 

11.  3  is  i  of  ? 


3  is  1  of  ? 
3  is  i  of  ? 


3  is  I  of  ? 

4  is  ^  of  ? 
4  is  4  of  ? 


What  part  of  15  is  5  ? 
What  part  of  15  is  3? 
What  part  of  1 5  is  9  ? 
What  part  of  15  is  10? 
What  part  of  15  is  12  ? 

5  is  ^  of  ? 

5  is  J  of  ? 

6  is  i  of  i 


54 


THE   RATIONAL   ARITHMETIC. 


PART   FIRST.  55 

1.  Wliat  are  the  dimensions  of  the  red  rectangle? 

2.  What  is  its  area? 

3.  How  many  rows  of  6  square  inches  are  there  in  the 

rectangle  ? 

4.  What  part  of  the  area  is  one  row?     What  part  is 

two  rows  ? 

5.  How  many  rows  of  3  square  inches  are  there  in  the 

rectangle  ? 

6.  What  part  of  the  area  is  one  row?     What  part  is 

two  rows  ?   Three  rows  ?   Four  rows  ?    Five  rows  ? 

7.  What  part  of  the  area  is  1  square  inch?    What  part 

is  2  square  inches?     3  square  inches?     9  square 
inches?     10  square  inches? 

8.  How  many  two -inch  squares  can  be  cut  from  the 

rectangle  ?     How  many  can  be  made  fi^om  it  ? 

9.  How  many  three -inch  squares  can  be  cut  from  the 

rectangle  ? 

10.  How  many  rectangles  2  inches  long  and  1  inch  wide 

can  be  made  fi'om  the  i*ed  rectangle  ? 

11.  How  long  is  the  perimeter  of  the  red  rectangle ; 

12.  9  and    9  are 18  -     9  = 

6  and  12  are 18  -     6  = 

3  and  15  are 18  —     3  = 

10  and  8  are 18  -  12  = 

13.  In  18  there  are  how  many  6's  ?  What  part  of  18  is  6  ? 
In  18  there  are  how  many  3's  ?  What  part  of  18  is  3  ? 
In  18  there  are  how  many  9's  ?  What  part  of  18  is  9  ? 
In  18  there  are  how  many  2's  ?    What  part  of  18  is  2  ? 

14.  How  many  3's  in  3?  How  many  3's  in  12? 
How  many  3's  in  6  ?  How  many  3's  in  15  ? 
How  many  3's  in  9?  How  many  3's  in  18? 


56 


THE   RATIONAL   ARITHMETIC. 


1.  What  is  the  length  of  one  side  of  the  orange  square? 

2.  How  many  rows  of  square  inches  are  there  in  its 

surface  ? 

3.  One  row  is  what  part  of  the  surface?     Two  rows 

are    what   part?       Three    rows    are    what   part? 
Four  rows  are  what  part  ? 

4.  How  many  square  inches  are  there  in  each  row  ? 

5.  How  many  square  inches  are  there  in  the  entire  area  ? 

6.  1  square  inch  is  what  part  of  a  row  ?    2  square  inches 

are  what  part?     3  scpiare  inches  are  what  part? 


PART   FIRST.  57 

1.  1  square  inch  is  what  part  of  the  entire  area?     2 

square  inches  are  what  part?  3  square  inches 
are  what  part?  4  square  inches?  8  square 
inches?     12  square  inches? 

2.  How  many  two -inch  squares  can  be  made  from  the 

orange  square?     How  many  three -inch  squares? 

3.  How  many  rectangles  2  inches  long  and  1  inch  vnde 

can  be  made  from  the  orange  square  ? 

4.  How  many  rectangles  3  inches  long  and  1  inch  wide 

can  be  made  from  it  ?  How  many  rectangles  3 
inches  long  and  2  inches  wide  ? 

5.  How  many  4  square  inches  in  a  four-inch  square? 

How  many  8  square  inches  ?     How  many  2  square 
inches?     3  square  inches?     5  square  inches?     7 
square  inches  ?     6  square  inches  ? 
(\.  Draw  a  four -inch  square. 

7.  Take  away  one  row  of  square  inches.     How  many 

square  inches  are  left  ? 

8.  Take  away  two  rows.     How  many  square  inches*  are 

left  ?  Take  away  three  rows.  How  many  square 
inches  are  left? 

9.  Draw  rectangles  containing  16  square  inches. 

10.  4  and  12  are 16  -  8  = 

8  and  8  are 16  —  4  = 

6  and  10  are 16  —  6  — 

14  and  2  are 16  -  2  = 

11.  What  part  of  16  is  4?  12  is  f  of  ? 
What  part  of  16  is  8  ?  6  is  f  of  ? 
What  part  of  16  is  12  ?  4  is  i  of  ? 
What  part  of  16  is  2  ?  2  is  i  of  ? 
What  part  of  16  is  6  ?  8  is  4  of  ? 


58  THE   RATIONAL   ARITHMETIC. 


*i 


1.  What  are  the  dimensions  of  the  yellow  rectangle? 

2.  How  many  rows  of  5  square  inches  are  there  in  the 

rectangle?     What  j^art  of  the  area  is  one  row? 
Two  rows  ? 


PART  FIRST.  50 

1 .  How  many  rows  of  4  square  inclies  are  there  in  the 

yellow  rectangle  ?  What  part  of  the  area  is  one 
row  ?     Two  rows  ?     Three  rows  ? 

2.  1  square  inch  is  what  part  of  a  four-inch  row?     Of 

a  five -inch  row?  Of  the  entire  area?  5  square 
inches  are  what  part?  10  square  inches?  8 
square  inches? 

3.  How  many  two -inch  squares  can  be  cut  from  the 

yellow  rectangle?  How  many  can  be  made 
from  it? 

4.  How  many  three -inch  squares  can  be  made  from  the 

rectangle  ?     How  many  four-inch  squares  ? 

5.  If  one  row  of  5  square  inches  were  taken  aw^ay  from 

the  yellow  rectangle,  how  many  square  inches 
would  be  left?  If  two  rows  were  taken  away, 
how  many  square  inches  would  be  left  ? 

6.  If  one  row  of  4  square  inches  were  taken  away  from 

the  yellow  rectangle,  how  many  square  inches 
would  be  left?  If  two  rows  were  taken  away, 
hoAY  many. square  inches  would  be  left? 

7.  Draw  other  rectangles  containing  20  square  inches. 

8.  5  and  15  are 20  —  15  = 

10  and  10  are 20  -  S  = 

4  and  16  are 20  -  10  = 

8  and  12  are 20  -  4  = 

9.  What  part  of  20  is  5  ?  4  is  |  of  ? 
What  part  of  20  is  15  ?  12  is  I  of  ? 
What  part  of  20  is  4  ?                           5  is  J  of  ? 
What  part  of  20  is  8  ?                           8  is  f  of  ? 
What  part  of  20  is  10?  10  is  i  of  ? 
What  part  of  20  is  16  ?  15  is  |  of  ? 


60 


THE  RATIONAL  ARITHMETIC. 


PART   FIRST. 


Gl 


1.  What  are  tlie  dimensions  of  the  green  rectangle? 

2.  What  is  its  area? 

3.  How  many  rows  of  6  square  inches  are  there  in  its 

surface  ?     What  part  of  its  area  is  one  row  ?    Two 
rows?     Three  rows? 

4.  How  many  rows  of  4  square  inches  are  there  in  the 

rectangle?      What  part  of  its  area  is  one  row? 
Two  rows?     Three  rows? 

5.  What  part  of  the  area  of  the  rectangle  is  1  square 

inch  ?     What  part  is  2  square  inches  ?     3  square 
inches?     4  square  inches?     6  square  inches? 

6.  How  many  two -inch  squares  can  be  cut  from  the 

green  rectangle?     How  many  three-inch  squares? 
How  many  four-inch  squares? 

7.  What  rectangles  can  be  cut  or  made  from  the  green 

rectano^le  ? 


8. 


12  and  12  are 
18  and  6  are  _ 
14  and  10  are 
16  and  8  are  _ 


9.  What  part  of  24  is  3? 
What  part  of  24  is  4  ? 
What  part  of  24  is  2  ? 
What  part  of  24  is  12? 
What  part  of  24  is  8  ? 
What  part  of  24  is  6  ? 

10.  How  many  4's  in  4? 
How  many  4's  in  8  ? 
How  many  4's  in  12  ? 

11.  How  many  5's  in  5? 
How  many  5's  in  10? 


24  -  16  - 

24  -  12 

24  -  10  - 

24-6 

i  of  24  = 

1  of  24  = 

4  of  24 

I  of  24 

i  of  24  - 

tV  of  24  = 

How 

many  4's  in  16? 

How 

many  4's  in  20? 

How 

many  4's  in  24  ? 

How 

many  5's  in  15? 

How 

many  5's  in  20? 

62 


THE   RATIONAL   ARITHMETIC. 


Draw  figures  to  illustrate  areas  of  rectangles  that  are 

2  inclies  by  2  inclies.     1x4.     4x5.    4x6.  2x6. 

3  inclies  by  3  inclies.     5X2.     3.x  6.    2  X  10.  1  x  5. 

4  inches  by  2  inches.     4x4.     5x4.     1x6.  3x8. 
3  inches  by  4  inches.     5X3.     3x1.    4X3.  3x2. 

What  are  the  areas  of  rectangles  that  are 
3  inches  by  7  inches?     5x8?       4  x  10? 


3X9? 
4X9? 
5X9? 
3  X  10? 


5  X  10? 

3  X  11? 

4  X  11? 

5  X  11? 


4  inches  by  7  inches  ? 

5  inches  by  7  inches  ? 

3  inches  by  8  inches  ? 

4  inches  by  8  inches  ? 
What  is  the  width  of  a  rectangle  that  contain? 

4  square  inches,  and  is  2  inches  long  ? 

6  square  inches,  and  is  3  inches  long  ? 
9  square  inches,  and  is  3  inches  long  ? 
12  square  inches,  and  is  4  inches  long? 
8  square  inches,  and  is  4  inches  long  ? 
24  square  inches,  and  is  8  inches  long  ? 


X  12? 
X  12? 
X  12? 

X  5? 
5X6? 


3 
4 
5 
5 


s 


10  square  inches 
18  square  inches 
12  square  inches 
24  square  inches 
16  square  inches 
18  square  inches 

14  square  inches 

24  square  inches 

15  square  inches 
20  square  inches 

25  square  inches 
30  square  inches 
20  square  inches 


and  is  5  inches  lono-? 
and  is  6  inches  long? 
and  is  6  inches  long  ? 
and  is  6  inches  long  ? 
and  is  8  inches  long  ? 
and  is  9  inches  long  ? 
and  is  7  inches  long  ? 
and  is  12  inches  long? 
and  is  5  inches  long? 
and  is  4  inches  long  ? 
and  is  5  inches  long  ? 
and  is  6  inches  long  ? 
and  is  10  inches  long? 


PART   FIRST.  63 

1.  Draw: 

A  line  1  iiicli  long. 

A  line  tmce  as  long  as  the  first  line. 

A  line  three  times  as  long  as  the  first  line. 

A  line  twice  as  long  as  the  second  line. 

A  square  mth  each  of  its  sides  the  length  of  the 

first  line. 
A  square  w^ith  each  of  its  sides  the  length  of  the 

second  line. 
A  square  mth  each  of  its  sides  the  length  of  the 

third  line. 
A  square  with  each  of  its  sides  the  length  of  the 

fourth  line. 

2.  ITow  many  square  inches  are  there  in  each  square? 
8.  The  area  of  the  one -inch  square  equals  what  jiart  of 

the  area  of  the  other  s([uares? 

4.  The  area  of  the  two-inch  square  is  how  many  times 
that  of  the  one -inch  square?  It  equals  what  jiart 
of  the  area  of  the  three-inch  S(]^uare?  Of  the 
four -inch  square? 

T).  The  area  of  the  three -inch  square  is  how  many 
times  that  of  the  one-inch  square?  Of  the  two- 
inch  square?  It  equals  what  jDart  of  the  area  of 
the  four -inch  square? 

(k  Tiie  area  of  the  four-inch  square  is  how  many  times 
that  of  the  otlier  squares? 

7.  How  many  two -inch  squares  can  he  made  from  the 
three-inch  square?     From  the  four-inch  square? 

Note  —  By  means  of  square  measure,  the  tables  may  be  taught ;  ^.  e., 
liow  many  square  inches  in  a  rectangle  2  by  2  inches,  2  by  3  inches,  2  by  4 
inches?  etc,  or,  how  long  is  a  rectangle  that  contains  4  square  inches,  and 
is  2  inches  wide?    That  contains  0  square  inches  and  is  2  inches  wide? 


64 


THE   RATIONAL   ARITHMETIC. 


j 

A 

P! 

/-» 

— 

n 

A 

' 

D 

L» 

U 

F 

p- 

/^ 

H 

L. 

r 

u 

n 

) 

1 

1 

\{ 

1 

D 

U 

l\ 

L. 

1 

1 

1.  Compare  each  figure  with  eacQi  of  the  other  figures. 

2.  A  is  5.     How  many  5\s  in  B  ?     How  manv  in  C  ?     In 

D?    E?     F?     G?    H?    I?    J?     K? 'l? 

3.  A  equals  5,  B  equals  10.     To  what  is  C  equal?     D? 

E?    F?     G?    H?    I?    3i    K?    L? 


PART   illlST.  65 

1.  A  equals  what  part  of  B?     What  part  of  C?     Of 

D?    E?    F?     G?    H?    I?    J?     K?    L? 

2.  5  is  what  part  of  10?     What  part  of  15?     Of  20? 

25?     80?     85?     40?     45?     50?     55?     60? 
:\.   B  equals  how  many  A's  ?     What  part  of  C  ?     Of  D  ? 
E?    F?     G?    H?    I?    J?    K?    L? 

4.  10  is  how  many  5V?     What  part  of  15?     Of  20? 

25?     80?     85?     40?     45?     50?     55?     60? 

5.  G  equals  how  many  A's?     How  many  B's?     What 

partofD?    OfE*^?    F?    G?    H?    I?    J?    K?    L? 

6.  15  is  how  many  5's?     How  many  lO's?     What  part 

of  20?    Of  25?    30?    85?    40?    45?    50?    55?    60? 

7.  D  equals  how  manyA's?     How  many  B's?     How 

many  C\s?     What  part  of  E?     Of  F?     G?     H? 
I?    J?    K?    L? 

8.  20  is  how  many  5's?     How  many  10\s?     How  many 

15's?    What  part  of  25  ?    Of  80?    85?    40?     45? 
50?     55?     60? 

9.  E  equals  how  many  A's?     How  many  B's?     How 

many  C's?     How  many  D's?     What  part  of  F? 
OfG?    H?    I?    J?    K?    L? 

10.  25  is  how  many  5 's?     How  many  lO's?     How  many 

15's?     How  many  20\s?     What  part  of  80?     Of 
85?     40?     45?     50?     55?     60? 

11.  F  equals  how  manyA's?     How  many  B's?     How 

many  C's?      How  many  D's?      How  many  E's? 
What  part  of  G?     OfH?     I?     J?     K?     L? 

12.  80  is  how  many. 5's?     How  many  lO's?     How  many 

15's  ?    How  many  20's  ?    How  many  25\s  ?    What 
part  of  85?     Of  40?     45?     50?     55?     60? 
18.  G  equals  how  many  A's ?     How  many  B's?     Etc. 


G6 


THE   RATIONAL   ARITHMETIC. 


DRILL   TABLES. 


2x1- 

2  - 

-  2 

— 

1 

2 

of  4 

3 

X  2  ■- 

2x8- 

24  - 

-  2 

1 
2 

of  8  - 

3 

X  12 

2X5- 

4  - 

.  2 

1 
2 

of  1 2  - 

3 

X  4  - 

2X7=- 

22  - 

r-    2 

1 
2 

of  16 

3 

X  10 

2X9 

6  - 

-  2 

1 
2 

of  20  = 

3 

X  6  - 

2  X  11  - 

20  - 

-  2 

— 

1 
2 

of  24  - 

3 

X  8  : 

2X2- 

8  - 

-  2 

1 
2 

of  2 

3 

X     1    : 

2X4  = 

18  - 

-  2 

— 

1 
2 

of  6  = 

3 

X     11 

2X6 

10  - 

-  2 

1 

2 

of  10 

3 

X  3  ■- 

2X8- 

16  - 

^  2 

— 

1 
2 

of  14  - 

3 

X     9    : 

2  X  10 

12  - 

-  2 

i 

of  18 

3 

X     5    : 

2  X  12  - 

14  - 

-  2 

1 
2 

of  22  = 

3 

X    7    : 

3  - 

-  3 

1 

3 

of  6  - 

2. 
3 

of  6  - 

4 

X    1    : 

9  -^ 

-  3 

— 

1 
3 

of  12  - 

2 
3 

of  12 

4 

X     3    : 

15  - 

-  3 

1 
3 

of  18  - 

2 
3" 

of  18  = 

4 

X  5  ■- 

21  - 

-  3 

i 

of  24 

of  24 

-: 

X  7  ■■ 

27  - 

-  3 

1 
3 

of  30  - 

2 
3 

of  30  - 

4 

X   9  : 

33  - 

-  3 

— 

i 

of  36  - 

1 

of  36 

4 

X  11 

6  - 

r    3 

— 

1 
3 

of  3  = 

2 

of  3 

4 

X     2    : 

12  - 

-  3 

— 

1 

3 

of  V)  = 

2 

of  9 

■:: 

X  4  = 

18  - 

r    3 

— 

1 

3 

of  15  - 

2 

3 

of  15 

4 

X  6  = 

24  - 

:-    3 

1 
"3^ 

of  21  - 

3 

of  21  - 

4 

X  8  - 

30  - 

'r-    3 

1 

of  27  = 

2 
3 

of  27  = 

4 

X  10 

36  - 

^-  3 

— 

1 

"3: 

of  33  - 

2 
"3 

of  33 

4 

X  12 

PART   FIRST. 


67 


DRILL   TABLES. 


8  - 

-  4 

16  " 

i-  4 

24  - 

-  4 

32  - 

-  4 

40  - 

-  4 

48  H 

-  4 

4  H 

-  4 

12  -. 

-  4 

20  - 

-  4 

28  -^ 

-  4 

36  - 

-     -: 

44  - 

-  4 

i  of  4 

1  of  4  = 

5 

XI- 

1  of  12 

i  of  12  = 

5 

X  4 

1  of  8 

i  of  8  - 

5 

X  2 

i  of  16  = 

i  of  16 

5 

X  5 

1  of  24  - 

i  of  24 

5 

X  3  - 

1  of  32 

f  of  32  - 

5 

X  6  = 

1  of  20 

f  of  20 

5 

X  9  - 

1  of  28  - 

i  of  28 

5 

X  7  = 

i  of  36  = 

i  of  36  - 

5 

X  8 

I  of  48 

1  of  48  = 

5 

X  12  = 

iof  40 

f  of  40  - 

5 

X   10  -- 

i  of  44  = 

i  of  44  - 

5 

X   11  = 

10  - 

-  5 

25  -^ 

-  5 

40  - 

-  0 

5  - 

-  5 

20  - 

-  5 

55  -■ 

15  -• 

-  5 

30  - 

-  5 

45  - 

^  5 

35  - 

'-    0 

60  - 

h  5 

50  - 

h  5 

-i-ofS- 

|of5- 

4  of  5    : 

4  of  20  =-- 

f  of  20  = 

4  of  20 

4  of  10  - 

1-  of  10  = 

4  of  10 

4  of  25 

-1  of  25  = 

4  of  25 

i  of  15  - 

I  of  15  = 

4  of  15 

4  of  30  = 

1  of  30  - 

4  of  30 

I  of  60 

1  of  60  - 

4  of  60 

4- of  35 

1  of  35 

4  of  35 

Iof  55 

f  of  55  = 

4  of  55 

4  of  40  - 

1  of  40 

4  of  40 

I  of  50  - 

*j 

1  of  50 

4  of  50 

1  of  45  - 

1  of  45  - 

4  of  45 

08 


THE   RATIONAL   ARITHMETIC. 


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PART   FIRST.  69 

1.  Place  two  one-incli  cubes  in  a  row. 

2.  Place  another  row  of  two  one- inch  cubes  in  front  of 

the  first  row. 

3.  How  many  rows  of  one-inch  culjes  are  there? 

4.  How  many  one-inch  cubes,  or  cul)ic  inches,  are  there 

in  a  row  ?     How  many  are  there  in  both  rows  ? 

5.  Place  four  more  one -inch  cubes  on  top  of  these  cubes. 

6.  How  many  layers  of  cubes  are  there? 

7.  How  many  cubic  inches  are  there  in  a  layer?     How 

many  are  there  in  both  layers? 

8.  Find  a  two -inch  cube. 

9.  Build  a  two-inch  culx'  with  the  one-inch  cubes. 

10.  How  many  layers  of  one -inch  cubes  are  there  in  the 

two -inch  cube? 

11.  How  many  rows  are  there  in  each  layer  ? 

1'2.  How  many  one -inch  cubes  are  there  in  each  row? 
VS.  How  many  one -inch  cubes  are  there  in  both  rows? 

14.  How  many  one-inch  cubes  are  there  in  both  layers? 

15.  Take  away  one  layer  of  cubes. 

16.  How  many  one -inch  cubes  are  taken?     What  part 

of  the  two -inch  cube  is  taken? 

17.  Take  away  one  row  from  the  remaining  layer. 

18.  What  part  of  the  layer  is  taken?     What  part  of  the 

two-inch  cube  is  taken  ? 

19.  Take  away  a  one -inch  cube  from  the  remaining  row. 

20.  What  part  of  the  row  is  taken  ?     What  part  of  the 

layer  is  taken?     What  part  of  the  two -inch  cube  ? 

21.  A  one-inch  cube  is  what  part  of  a  two-inch  cube? 

Two  one -inch  cubes  are  what  part?  Three  one- 
inch  cubes  are  w^hat  part?  Four  are  what  part? 
Five  ? 


70  THE   RATIONAL   ARITHMETIC. 

{Refer  to  figures  on  page  68  and  use  solids.) 

1.  In  a  two-inch  cube  there  are  how  many  one -inch 

cubes  ? 

2.  In  one -half  of  a  two -inch  cube  there  are  how  many 

one -inch  cubes? 

3.  In  one -half  of   one -half  of  a  two -inch  cube,  how 

many  one -inch  cubes  are  there?     What  part  of 
the  two-inch  cube  are  these  one-inch  cubes? 

4.  One-fourth  is  what  part  of  one-half? 

5.  Point  out  one-fourth  of  the  two-inch  cube. 

6.  Point  out  three -fourths  of  the  two -inch  cube. 

7.  Point  out  on^ -third  of  three -fourths  of  the  two -inch 

cube. 

8.  What  part  of  the  two -inch  cube  is  one -third  of  three- 

fourths  of  it?     What  part  is  two-thirds  of  three- 
fourths  of  it  ? 

9.  What  part  of  one-half  of  the  two-inch  cube  is  a  one- 

inch  cube?      What  j)art  is  two  one-inch  cubes? 
Three  one -inch  cubes? 

10.  What  part  of  the  two-inch  cube  is  one-fourth  of 

one-half  of  it?    Two-fourths  of  one-half?    Three- 
fourths  of  one-half? 

11.  One -eighth  is  what  part  of  one -fourth? 

12.  One-eighth  is  what  j)art  of  one-half? 

13.  One-eighth  is  what  part  of  three -fourths? 

14.  Two -eighths  are  what  part  of  three -fourths? 

15.  One-half  equals  how  many  fourths? 

16.  One-half  equals  how  many  eighths? 

17.  One -fourth  equals  how  many  eighths? 

18.  Three-fourths  equal  how  many  eighths? 

19.  One-third  of  three-fourths  equals  how  many  eighths  ? 


PART    FIRST.  71 

1.  Build  with  cubes  a  solid  that  is  equal  to  two  rows 

of  3  cubic  inches. 

2.  What  are  its  dimensions? 

3.  Build  a  solid  tliat  is  equal  to  t\\  o  layers  of  two  rows 

of  3  cubic  inches. 

4.  What  are  its  dimensions? 

5.  Build   the  following  solids,  tell    their  dimensions, 

and  the  number  of  cubic  inches  in  each: 
One  layer  of  two  rows  of  3  cubic  inches. 
Two  layers  of  two  rows  of  3  cubic  inches. 
One  layer  of  two  rows  of  4  cubic  inches. 
Two  layers  of  two  rows  of  4  cubic  inches. 
One  layer  of  three  rows  of  5  cubic  inches. 
Two  layers  of  two  rows  of  5  cubic  inches. 
Two  layers  of  one  row  of  8  cubic  inches. 
Two  layers  of  one  row  of  7  cubic  inches. 
Four  layers  of  one  row  of  4  cubic  inches. 
Two  layers  of  one  roAv  of  6  cubic  inches. 
Two  layers  of  three  rows  of  3  cubic  inches. 
Four  layers  of  one  row  of  5  cubic  inches. 
Three  layers  of  two  rows  of  4  cubic  inches. 
Four  layers  of  three  rows  of  2  cubic  inches. 
One  layer  of  three  rows  of  8  cubic  inches. 
Two  layers  of  one  row  of  9  cubic  inches. 
One  layer  of  two  rows  of  12  cubic  inches. 
0.  Give  the  dimensions  of  solids  containing: 

8  cubic  inches.  12  cubic  inches. 
6  cubic  inches.  10  cubic  inches. 

9  cubic  inches.  16  cubic  inches. 

Note. — Have  the  pupils  handle  various  solids  and  estimate  their  length, 
breadth,  and  height.     After  estimating,  measure. 


72 


THE   RATIONAL   ARITHMETIC. 


CUT    .                       ;    CUT 

OUT   ;                  1   our 

CUT    ;                       1    CUT 
OUT    .                         1    OUT 

1.  To  make  a  box  that  will  hold  4  cubic  inches,  draAv 

a  figure  like  the  illustration.  Cut  out  the  corners, 
fold  on  dotted  lines,  and  paste  the  square  pieces 
cut  from  the  corners,  over  the  joinings. 

2.  Make  a  box  that  will  hold 

6  cubic  inches.  15  cubic  inches. 

S  cubic  inches.  16  cubic  inches. 

10  cubic  inches.  18  cubic  inches. 

12  cubic  inches.  20  cubic  inches. 

14  cubic  inches.  24  cubic  inches. 


PART   FIRST.  73 

1.  A  box  is  three  inclies  long,  two  inclies  wide,  and 

two  inclies  liigh.     How  many  cubic  inches  will  it 
hold  ? 

2.  How  wide  is  a  box  that  contains  eight  cubic  inches, 

and  is  two  inches  high  and  two  inches  long  ? 

3.  How  long  is  a  box  that  contains  sixteen  cubic  inches, 

and  is  two  inches  wide  and  two  inches  hi2:h  ? 

4.  How   high    is    a   box    that    contains   twelve    cubic 

inches,  and  is  two  inches  long  and  two  inches  wide  ? 

5.  A  brick  six  inches  long  and  two  inches  wide  contains 

twentv-four  cubic  inches.     How  thick  is  it? 

6.  A  bin  is  four  feet  long,  two  feet  wide,  and  four  feet 

high.     How  many  cubic  feet  does  it  contain  ? 

7.  In  a  block  of  marble  there  are  sixteen  cu1:>ic  feet. 

It  is  four  feet  long  and   two  feet  wide.     How 
high  is  it? 

8.  A  ])ook  is  six  inches  long,  four  inches  wide,  and  one 

inch  thick.    Hoav  manv  cubic  inches  are  there  in  it  ? 

9.  How  many  cubic  feet  will  a  glass  case  hold  that  is 

fiYQ  feet  high,  two  feet  wide,  and  two  feet  long? 

10.  How  many  cul)ic  yards  are  there  in  a  room  that  is 

three   yards    long,    two    yards    ^vdde,    and    three 
yards  high  ? 

11.  A  ditch  is  four  feet  mde  and  three  feet  dee^D.    How 

many  cubic  feet  are  there  in  a  part  two  feet  long? 
How  many  in  a  part  three  feet  long? 

12.  How  many  cubic  yards  will  a  wagon  box  hold  that 

is  three  yards  long,  two  yards  wide  and  one  yard 
high? 
18.  How  many  cubic  feet  are  there  in  a  pile  of  wood 
four  feet  long,  two  feet  wide,  and  two  feet  high  ? 


74 


THE    RATIONAL   ARITHMETIC. 


Igill  4  gills  8  gills  32  gills 

1  pint  2  pints  8  pints 

1  quart  4  quarts 

1  gallon 

1.  What  is  sold  by  tlie  gill  ? 

2.  Measure  and  find  how  many  gills  in  a  pint. 
8.  One  pint  equals  how  many  gills? 

4.  One  gill  equals  what  part  of  a  pint?      Two  gills 

equal  what  part?     Three  gills  equal  what  part? 

5.  One  and  one -half  pints  equal  how  many  gills? 

6.  If  a  pint  of  Avater  weighs  a  pound,  how  much  will  a 

gill  weigh  ?     How  much  will  three  gills  weigh  ? 

7.  What  is  sold  by  the  pint  and  quart? 

8.  Measure  and  find  how  many  pints  in  a  quart. 

9.  One  quart  equals  how  many  pints? 

10.  One  pint  equals  what  part  of  a  quart? 

11.  IIow  many  gills  are  there  in  one-half  of  a  quart? 

How  many  are  there  in  a  quart  ? 

12.  One  and  one-half  quarts  equal  how  many  joints? 
18.  If  a  })int  of  water  weighs  a  pound,  how  much  will 

a  quart  weigh  ? 

14.  What  is  sold  by  the  gallon? 

15.  Measure  and  find  how  many  quarts  in  a  gallon. 


PART   FIRST.  75 

1.  One  gallon  equals  how  many  quarts? 

2.  One  quart  equals  wliat  part  of  a  gallon?      Two 

quarts   equal    what   part?       Three  quarts   equal 
what  part? 

3.  One  and  one-half  gallons  equal  hoAV  many  quarts? 

4.  If  a  quart  of  water  weighs  two  pounds,  how  much 

will  a  gallon  weigh  ? 

5.  How  many  quarts  are  there  in  one -half  of  a  gallon? 

In  one-fourth? 
0,  How  many  pints  are  there  in  one-fourth  of  a  gallon? 
How  many  are  there  in  a  gallon? 

7.  How  many  gills  are  there  in  one-fourth  of  a  gallon? 

8.  Tell  how  many  gills  equal  two  pints;  one  and  one- 

half  pints;  two  quarts. 

9.  Tell  how  many  pints  equal  three  quarts;  two  and 

one -half  quarts;  two  gallons. 

10.  Tell  how  many  quarts  equal  two  gallons. 

11.  At  24  cents  a  quart,  how  much  will  a  |)int  of  mo- 

lasses cost? 

12.  How  much  will  a  gallon  of  milk  cost  at  6  cents  a 

quart  ? 

13.  How  much  will  a  quart  of  cream  cost  at  4  cents  a 

gill? 

14.  A  can  holds  twelve  quarts;  how  many  gallons  ^vill 

it  hold  ? 

15.  How  many  quarts  does  a  three-gallon  jug  hold? 

1<>.  How  many  quarts  of  milk  are  there  in  sixteen  pints? 

In  twenty  pints?     In  twenty -four  pints? 
17.  A  boy  had  two  gallons  of  mineral  water,  and  sold 

four  pints  of  it.     How  many  pints  had  he  left? 

How  many  gallons? 


76 


THE   RATIONAL   ARlTHxMETIC. 


1  pint 


2  pints 
1  quart 


16  pints 
8  quarts 
1  peck 


64  pints 
32  quarts 
4  pecks 
1  bushel 

1.  What  articles  are  sold  by  tlie  bushel? 

2.  Find  by  measuring  how  many  pecks  there  are  in  a 

bushel. 

3.  One  peck  equals  what  part  of  a  bushel  ? 

4.  One-half    of    a   bushel    equals    how   many  pecks? 

One-fourth  of  a  bushel  equals  how  many  pecks? 
Three-fourths  equal  how  many  pecks? 

5.  How  many  pecks  are  there  in  one  and   one-half 

bushels  ? 

6.  Find  by  measuring  how  many  quarts  there  are  in 

one  peck. 

7.  One  quart  equals  what  j)art  of  a  peck? 

8.  Put  four  quarts  into  the  peck  measure. 

part  of  the  measure  is  filled. 

9.  Two  quarts  equal  what  part  of  a  peck? 

equal  what  part  ? 

10.  How  many  quarts  are  there  in  one  and  one -half 

pecks  ? 

11.  How  many  quarts  fill  a  bushel  measure? 

12.  One  quart  e([uals  what  part  of  a  bushel? 


Tell  what 


Six  quarts 


PART  FIRST.  77 

1.  How  many  pints  are  there  in  a  quart?     In  eight 

quarts?     In  thirty-two  quarts? 

2.  How  many  pints  are  there  m  a  peck?     In  one-half 

of  a  peck?     In  one -fourth  of  a  peck? 

3.  How  many  bushels  do  twelve  pecks  equal  ?     Sixteen 

pecks  ?     Twenty  pecks  ? 

4.  How  many  pecks  do  sixteen  quarts  equal  ?     Thirty - 

two  quarts? 

5.  At  8  cents  a  quart,  what  mil  six  pints  of  cranber- 

ries cost? 

6.  If  cherries  cost  10  cents  a  quart,  what  will  one -half 

of  a  peck  cost  ? 

7.  A  boy  picked  one  and  one-half  bushels  of  cherries. 

He  sold  them  by  the  peck;  how  many  pecks  did 
he  sell  ?  How  many  dollars  did  he  receive  for 
them  at  one-half  dollar  for  a  peck? 

8.  How  many  bags  holding  one  bushel  each  will  be 

required  to  hold  twenty -four  pecks  of  corn  ?  How 
many  holding  two  bushels  each  will  be  required  ? 

9.  At  4  cents  a  quart  what  will  a  peck  of  beans  cost? 

What  will  three-fourths  of  a  peck  cost? 

10.  If  there  are  ten  bushels  of  wheat  in  a  bin  and  twenty 

pecks  are  taken  out,  how  many  pecks  are  left? 
How  many  bushels  are  left  ? 

11.  A  man  can  dig  five  bushels  of  potatoes  in  one  hour. 

How  many  pecks  can  he  dig  in  two  hours  ? 

12.  If  oats  cost  30  cents  a  bushel,  what  will  two  pecks 

cost? 

13.  A  can  holds  sixteen  quarts  of  berries.     Ten  pints  of 

berries  are  taken  out;  how  many  pints  are  left? 
How  many  quarts  are  left? 


78 


THE   RATIONAL   ARITHMETIC. 


1  ounce      4  ounces    8  ounces 


16  ounces 
1  pound 


2  pounds 


3  pounds 


4  pounds 


1 .  One  pound  equals  how  many  ounces  ? 

2.  The  one- ounce  weight  equals  what  part  of  the  pound 

weight  ? 

3.  Two  one -ounce  weights  together  equal  what  part  of 

the  pound  weight? 

4.  The   four -ounce  weight   equals  what  part   of   the 

pound  weight? 

5.  The  eight- ounce  weight  equals  what  part  of  the 

pound  weight? 

6.  The  four-ounce  weight  and  the  eight-ounce  weight 

together  equal  what  part  of  the  pound  weight? 

7.  The  four -ounce  weight  and  two  one -ounce  weights 

together  equal  what  part  of  the  pound  weight? 

8.  The  eight -ounce  weight  and  two  one -ounce  weights 

together  equal  what  part  of  the  pound  weight? 

9.  What  part  of  the  two -pound  weight  does  a  one- 

ounce  weight  equal  ?    A  four-ounce  weight?    An 
eight-ounce  weight? 
10.  Four  eight- ounce  weights  together  equal  which  other 
weight? 

Note.— Have  bean  bags  of  different  sizes  holding  exact  weights,  as, 
four  pounds,  three  pounds,  two  pounds,  one  pound,  eight  ounces,  four 
ounces;  also,  sixteen  one-ounce  weights.  Have  the  pupils  estimate  the 
relation  of  the  weights  by  handling. 


PART   FIRST.  79 

1.  Wliicli  three  weights   together  equal  one  pound? 

Which  six  weights  ?  Which  nine  weights  ? 
2    Which  three  weights  together  equal  two  pounds? 

Which  four  weights  ?  Which  six  weights  ? 
8.  Give  three  ways  in  which   these   weights  may  be 

combined  to  equal  three  pounds.     Four  pounds. 

4.  At  6  cents  a  pound,  what  will  three  and  one -half 

pounds  of  sugar  cost? 

5.  How  many  four -ounce  jDackages  can  be  made  from 

three  pounds  of  tea  ? 

6.  How  many  jars,  each  holding  twelve  ounces,  can  be 

filled  from  one  and  one-half  pounds  of  butter? 

7.  What  is  the  weight  in  ounces  of  two  packages  of 

tea,  one  holding  three -fourths  of  a  pound,  and  the 
other  one -half  of  a  pound? 

8.  A  man  bought  two  pounds  of  salt  and  used  twenty - 

four  ounces  of  it.     How  many  ounces  had  he  left  ? 
What  part  of  a  pound  had  he  left  ? 

9.  If  cinnamon  costs  10  cents  an  ounce,  what  will  half 

a  pound  cost? 

10.  What  will  two  ounces  of  sunflower  seed  cost  at  40 

cents  a  pound  ? 

11.  If  one  pound  of  cofPee  costs  SG   cents,  what  Avill 

eight  ounces  cost? 

12.  What  will  one  pound   and   four  ounces  of  canarv 

seed  cost  at  2  cents  an  ounce? 
1?>.  If  one  pound  of   ])iitter  costs  24   cents,   what  anIII 

four  ounces  cost?     Twelve  ounces? 
14.  A  man  bought  two  pounds  of  rice,  and  sold  it  in 

eight-ounce  pack^xges,  at  8  cents  a  package.    How 

much  did  he  receive  for  the  rice? 


80 


THE   RxVnONAL   ARITHMETIC. 


5  nickels 


5  cents 


5  dimes 


4  quarters 


1  dollar 


2  half-dollars 


1.  How  many  cents  equal  a  nickel? 

2.  How  many  nickels  equal  a  dime?     How  many  cents 

equal  a  dime? 

3.  How  many  nickels  equal  a  quarter?      How  many 

cents  equal  a  quarter? 

4.  How  many  quarters  equal  a  half-dollar  ?    Hoav  many 

dimes  equal  a  half-dollar?     How  many  nickels 
equal  a  half-dollar? 

5.  How  many  half -dollars  equal  a  dollar?     How  many 

quarters  equal  a  dollar  ?     How  many  dimes  ? 

6.  Which  two  pieces  of  money  equal  a  dime? 

7.  Which  three  pieces  of  money  equal  a  quarter? 

8.  Which  two  pieces  of  money  equal  seventy-five  cents? 

Which  three  pieces? 

9.  Which  two  pieces  of  money  equal  a  dollar?    Which 

three  pieces  ?     Which  four  pieces  ? 

10.  To  how  many  quarters  are  two  dollars  equal  ?    Four 

dollars?     Five  and  one -half  dollars? 

11,  To  liow  many  half-dollars  are  six  quarters  equal  ? 


PART  FIRST.  81 

1.  A  boy  bought  a  top  for  25  cents,  and  paid  for  it  in 

nickels.     How  many  nickels  did  lie  spend  for  it? 

2.  A  book  wortk  30  cents  is  bought  with  a  half-dollar. 

How  many  dimes  are  needed  to  make  the  correct 
change  ? 

3.  A  package  of  flower  seed  costs  10  cents.    How  many 

quarters  Avill  pay  for  five  packages  ?  How  many 
dimes  ? 

4.  How  many   5 -cent    car  fares   can   be  paid  with  a 

quarter?     With  15  cents? 

5.  Harry  has  5  dimes  in  his  bank;  John  has  1  quarter 

and  2  dimes  in  his.     Which  has  the  more  money  ? 

6.  At  10  cents  each,  how  many  balls  can  be  bought 

for  a  quarter,  a  dime  and  a  nickel  together? 

7.  A  pound  of  candy  costs  50  cents.     How  much  can 

be  bought  for  1  dollar?  For  25  cents?  For  75 
cents?     For  5  cents? 

8.  How  many  50  cents  will  pay  for  a  chair  that  costs 

5  dollars? 

9.  A  sled  costs  1^  dollars.     How  many  25  cents  will 

be  required  to  pay  for  it  ? 

10.  Joe  bought  a  book  for  30  cents,  paper  for  25  cents, 

and  two  pencils  at  10  cents  each.  What  did  he 
pay  for  all  ?  What  two  pieces  of  money  would 
pay  for  them  ?     What  three  pieces  ? 

11.  If  a  gill  of  cream  costs  a  nickel,  how  many  dimes 

will  j)ay  for  a  quart  ? 

12.  If  three  dimes  pay  for  a  bushel  of  oats,  how  many 

nickels  will  pay  for  two  pecks? 

13.  If  one  pound  of  seed  costs  a  dollar,  what  part  of  a 

dollar  will  pay  for  four  ounces  ? 


82  THE   RATIONAL   ARITHMETIC. 

1.  Name  the  days  of  the  week. 

2.  How  many  days  are  there  in  one  week?      In  tAvo 

weeks  ?     In  three  weeks  ?     In  four  weeks  ? 
8.  What  part  of  the  week  is  one  day?     Two  days? 

4.  How  many  school  days  are  there  in  one  week  ?     In 

three  weeks?     In  ^ve  weeks? 

5.  How  many  days  of  the  week  are  not  school  days? 

6.  AVhat  j)art  of  the  week  is  the  school  days? 

7.  How  many  days  of  the  week  are  called  working 

days  ? 

8.  What  part  of  the  week  is  the  working  days? 

9.  How  many  weeks  are  there  in  a  month? 

10.  One  week  is  what  part  of  a  month?      Two  weeks 

are  what  part  ?     Three  weeks  are  what  part  ? 

1 1 .  Name  the  months  of  the  year  beginning  with  January. 

12.  How  many  months  are  there  in  the  year? 

18.  What  part  of  the  year  is  one  month  ?     Two  months  ? 
Six  months? 

14.  What   part    is    the    winter    months?       The    spring 

months?      The  summer  months?       The  autumn 
months  ? 

15.  During  what  months  is  school  held? 
IT).  What  2^ai't  of  the  year  is  school  held? 

17.  Dui'ing  what  months  is  there  vacation? 

18.  AVliat  part  of  the  year  is  there  vacation? 

19.  How  many  liours  are  there  in  a  day?     In  two  days? 

20.  AVliat  part   of  a  day  is  one  hour?     What  part  is 

two  hours?    Four  hours?    Ei£>:lit  hours?    Twelve 
hours  ? 

21.  How  many  houi's  are  called  "day"^      How  many 

are  called  "  sight "? 


PART   FIRST. 


83 


1.  Draw  tlie  face  of  a 
clock,  and  fasten  to 
the  center  two  mov- 
able hands. 

2.  Show  how  far  the  min- 
ute hand  moves  in  an 
hour.  Show  how  far 
the  hour  hand  moves 
in  an  hour. 

3.  How  many  minutes  are 
there  in  an  hour? 

4.  How  many  minutes  are  there  in  half  an  hour  ?    Ho^v 

many  in  one-fourth,  or  one-quarter,  of  an  hour? 

5.  Show  where  the  hands  are  at  one  oVlock. 

6.  Show  where  the  hands  are  at  thirty  minutes  after 

one,  or  half  past  one. 

7.  Show  where  the  hands  are  at  fifteen  minutes  after 

one,  or  quarter  j^ast  one. 

8.  Move  the  hands  to  show  the  time  of  the  opening  of 

school  in  the  morning;  the  beginning  of  recess; 
the  closing  of  school  at  noon;  the  opening  and 
closing  of  school  in  the  afternoon. 

9.  If  recess  lasts  fifteen  minutes,  what  imrt  of  an  hour 

does  it  last? 

10.  If  a  man  works  eight  hours  a  day,  what  part  of  a 

day  does  he  work  ? 

11.  A  boy  starts   for   school    at  twenty  minutes   after 

eight  and  arrives  there  at  ten  minutes  to  nine. 
How  long  is  he  on  the  way  ? 

12.  George  went  to  school  eight  months  one  year.    What 

part  of  the  year  did  he  attend  ? 


84  THE   RATIONAL  ARITHMETIC. 

1.  A  train  leaves   one   station   at   ten   minutes   after 

twelve,  and  arrives  at  tlie  next  at  half  past 
twelve;  how  many  minutes  does  it  take  to  go 
from  one  station  to  the  other?  What  part  of  an 
hour  ? 

2.  A  man  closes  his  store  and  starts  for  home  at  six 

o* clock.  He  walks  home  in  a  quarter  of  an  hour. 
What  time  is  it  when  he  arrives  ? 

3.  A  man  begins  work  at  eight  o'clock,  and  stops  at 

half  past  five.  How  many  hours  a  day  does  he 
work  if  he  stops  an  hour  at  noon  ? 

4.  Mary  is  six  years  old  and  Jennie  is  six  and  three - 

fourth  years  old.  How  many  months  older  is 
Jennie  than  Mary? 

5.  School  begins  at  nine  o'clock  and  closes  at  half  past 

three.  How  many  hours  are  there  between  the 
opening  and  the  closing?  An  hour  and  a  half 
are  allowed  at  noon,  and  half  an  hour  for  re- 
cesses; how  many  hours  are  the  pupils  in  school 
during  one  day? 

6.  A  farmer  OAvned  eighteen  horses.    He  sold  six;  how 

many  had  he  left  ?     What  part  had  he  left  ? 

7.  A  man  mailed  nine  letters  at  one  time  and  six  at 

another.     How  many  did  he  mail  altogether  ? 

8.  From  a  bunch  of  eighteen  bananas,  nine  bananas 

were  sold.     How  many  remained  on  the  bunch  ? 

9.  There  were  twenty  sheep  in  one  pen,  and  ten  m 

another.    How  many  in  both  ?    If  ^ve  were  taken 
out,  how  many  remained  in  the  pens  ? 
10    A  boy  paid  a  dime  for  a  bat,  and  a  nickel  for  a  ball. 
How  many  cents  did  he  pay  for  both  ? 


PART    FIRST.  85 

1.  How  long  a  string  will  reacli  around  the  frame  of  a 

slate,  tliat  is  twelve  inches  long  and  eight  inches 
wide  ? 

2.  A  box  two  inches  high  is  twice  as  wide  as  it  is  high. 

How  wide  is  it  ?     Its  length  equals  the  sum  of  its 
mdth  and  height.     How  long  is  it  ? 

3.  By  cleaning  walks,  Edwin  earned  a  quarter  on  Mon- 

day, a  dime  on  Tuesday,  and  a  nickel  on  Wednes- 
day.    How  much  did  he  earn  in  the  three  days  ? 

4.  One  jar  holds  four  pints,  another  holds  six  pints. 

How   many  pints   do   both   hold?      How  many 
quarts  do  both  hold  ? 

5.  A  ship  leaves   one  port   at   noon  on  Monday  and 

arrives  at  her  next  port  at  noon  on  Friday.     How 
many  days  was  she  on  the  way? 

6.  In  a  class  of  nineteen  pupils  there  was  one  more 

girl  than  there  were  boys.     How  many  girls  and 
boys  were  there  in  the  class  ? 

7.  A  car  goes  eight  miles  an  hour.     How  many  hours 

will  it  take  to  go  twelve  miles  ?     Twenty  miles  ? 
Sixteen  miles  ?     Twenty -four  miles? 

8.  Sixteen  acres  of  land  are  divided  into  two  equal 

fields.     How  many  acres  are  there  in  each  field  ? 

9.  When  it  is  a  quarter  past  nine  o'clock,  how  many 

minutes  past  nine  is  it  ? 

10.  How  many  pints  of  oil  are  there  in  a  can  holding 

twelve  quarts? 

11.  A  table  is  four  feet  long  and  two  feet  wide.     What 

is  the  length  of  its  perimeter  ?     What  is  its  area  ? 

12.  A  piece  of  sidewalk  seven  feet  long  contains  twenty- 

eight  square  feet.     How  wide  is  it? 


8G  THE   RATIONAL   ARITHMETIC. 

1.  If  a  peck  of  beans  costs  40  cents,  ^v^hat  will   one 

quart  cost? 

2.  How  many  four-(|uai't  pails  can  1)e  filled  from  seven- 

teen cpiarts  of  milk  ?  How  many  quarts  Avill  l)e 
left? 

3.  A  man  started  for  town  at  ten  minutes  to  nine,  and 

arrived  at  twenty  minutes  after  nine.  Ho^v  many 
minutes  Avas  lie  on  the  way?  What  part  of  an 
hour  was  he  on  the  Avay  ? 

4.  A  garden  five  rods  long  is  onedialf  as  wide  as  it  is 

long.  How  many  rods  of  fence  will  he  recpiired 
to  inclose  it? 

5.  A  grocer  bought  one  tub  of  butter  containing  ten 

pounds,  and  another  containing  five  pounds.  How 
many  pounds  did  he  buy?  How  many  jars  hokb 
ing  five  pounds  each  coukl  he  fill  with  the  butter? 

6.  Three   five-dollar   bills    equal    how  many   dollars? 

Four  five-dollar  bills?     Five  ten-dollar  bills? 

7.  When  16  cents  are  paid  for  twelve  eggs,  how  many 

cents  must  be  paid  for  six  eggs  ? 

8.  There  are  twenty  days  of  school  in  a  month.    Louis 

was  absent  ^ve  days.  What  part  of  the  school 
month  was  he  absent? 

9.  How  many  shoes  at  2  dollars  a  pair  can  be  bought 

for  15  dollars?     How  much  money  will  be  left? 

10.  The  rent  of  one  house  is  30  dollars  a  month;  the 

rent  of  another  is  one -half  as  much.  What  is  the 
rent  of  the  second  house?     Of  both  houses? 

11.  One  side  of  a  signboard  contains  thirty-six  square 

feet.  If  the  signboard  is  six  feet  high,  how  wide 
is  it?     If  it  is  nine  feet  high,  how  wide  is  it? 


PAKT   FIRST.  87 

1.  From  a  jug  holding  one  gallon  of  syru}),  one  (juart 

and  one  2)int  are  taken.        How  much  syrup  is 
left  in  the  jug? 

2.  How  many  Lags    holding   six  pecks  each  ^\'ill    he 

required  to  hold  six  Ijushels  of  corn? 

3.  A  train  leaves  one  station  at  fifteen  minutes  after  one 

and  arrives  at  the  next  station  half  an  hour  later. 
At  Avliat  time  does  it  reach  the  second  station  ? 

4.  What  is  the  Aveight  of  three  packages,  two  of  ^\  liich 

Aveigh  ten  ounces  each,  and  one,  five  ounces? 

5.  A  rectangular  field  containing  sixty  square  yards,  is 

twelve  yards  long.     Hoav  ^vide  is  it? 
(3.  If  one  pound  of  coffee  costs  32  cents,  what  Avill  four 
ounces  cost? 

7.  A  boy  left  home  at  eight  o'clock  in  the  morning  and 

returned  at  noon.    Ho^v  many  hours  was  he  a^vay  \ 
What  part  of  the  day  ^vas  he  a^vay  ? 

8.  If  a  rope  is  cut  into  four  equal  parts,  and  each  part 

is  three  feet  long,  ^vhat  was  the  length  of   the 
entire  rope? 

9.  In  a  basket  of  fruit  there  are  two  dozen  j^ears.     If 

half  a  dozen  are  taken  out,  ho^v  many  ^vill  be  left  ? 

10.  The  glass  in  a  picture  frame  is  two  feet  Avide  and 

three  feet  long.     How  many  s(piare  feet  are  there 
in  its  surface  ? 

11.  A  clock  is  fifteen  minutes  fast.    What  is  the  correct 

time  when  the  clock  says  half  past  three  ? 

12.  With  what  three  pieces  of   money  can  five  3 -cent 

car  fares  be  paid  ? 

13.  If  one  peck  of  potatoes  costs  25  cents,  what  Avill 

three  pecks  cost?     Four  pecks? 


88 


THE   RATIONAL  ARITHMETIC. 


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1.  How  many  squares  are  there  in  A? 

2.  How  many  figures  are  used  in  writing  the  number? 

3.  How  many  squares  are  there  in  B? 

4.  How  many  figures  are  used  in  writing  the  number? 

5.  How  many  figures  will  represent  C?     D?    E?    F? 

G?    H?     I? 

6.  How  many  lO's  in  A  and  how  many  over? 

7.  How  many  lO's  in  C? 

8.  How  many  lO's  in  D  and  how  many  over?     In  F? 

InG?     InH?     In  I? 

9.  Write  3  tens;  4  tens;  6  tens;  5  tens;  2  tens;  8  tens. 
10.  Write: 

2  tens  and  7. 

3  tens  and  7. 
5  tens  and  8. 
8  tens  and  2. 


3  tens  and  1. 

4  tens  and  2. 

5  tens  and  6. 
7  tens  and  5. 


2  tens  and  9. 

5  tens  and  1. 

6  tens  and  4. 
9  tens  and  1. 


PART   FIRST.  89 

1.  Add  A  and  B. 

A  equals  one  10  and  1,  or  11. 
B  equals  9. 

Place  tlie  9  squares  of  B  beside  the  1  A=ll 

of  A  and  wliat  do  we  have?  B=  9 

C  is  the  sum  of  A  and  B.  C=20 

2.  Add  D  and  E. 

Place  E  beside  the  6  of  D  and  what  D=16 

do  we  have?  E=  6 

F  is  the  sum  of  D  and  E.  F=22 

3.  Add  G  and  H. 

Place  the  3  of  H  by  the  8  of  G  and  G=18 

what  do  we  have  ?  H=13 

I  is  the  sum  of  G  and  H.  1=31 

4.  Add: 

A  and  D,  11           A  and  G,  11  A  and  H,  11 

16                              18  13 

D  and  H,  16           C  and  D,  20  C  and  G,  20 

13                             16  18 

C  and  H,  20           A  and  F,  11  A  and  E,  11 

13                             22  _6 

D  and  F,  16             G  and  I,  18  H  and  I,  13 

22                              31  31 

5.  Read  the  following  numbers:     21,  32,  44,  56,  27, 

46,  29,  45,  64,  36,  25. 

6.  Which  figure  tells  how  many  tens  in  each  number? 

7.  The  other  figure  we  will  call  ones,  as  1,  2,  4,  6,  7,  etc. 


00  THE   RATIONAL   ARITHMETIC. 

1.  Add:    11 
19^ 

10     [)  ones  and  1  are  10,  or  1  ten. 
2       1  ten  and  1  ten  are  2  tens. 


80 

o 

^ 

tens  and  1  ten 

are  8  tens  oi* 

80. 

2.  Add: 

15 

18 

18 
2 

88 

8. 

Add: 

26 
45 

11 
6 

71 

4.  Add: 

84 

29 

18 
5 

68 

) 

• 

5. 

Add: 

47 

89 

16 

7 

86 

1 

6.  Add: 

26 

17 

58 

84 

28 

25 

18 

32 

14 

87 

18 

27 

14 

26 

85 

29 

65 

76 

57 

89 

68 

58 

27 

46 

28 

16 

15 

48 

27 

29 

67 

89 

28 

85 

26 

14 

87 

49 

19 

16 

84 

15 

84 

49 

28 

88 

12 

59 

16 

46 

88 

29 

28 

15 

67 

28 

46 

84 

25 

82 

54 

87 

24 

84 

PART   FIRST.  91 

1.  Write  11  tens.     Read.      IIoav  many  hundreds? 
Write  12  tens.     Read.       How  many  linndreds  and 

how  many  tens  over  ? 
AVrite  15  tens.     Read.     How  many  hundreds  and 

how  many  tens  over? 
Write  4  tens  and  4. 
Write  14  tens  and  4.     Read.     How  many  hundreds, 

tens,  and  ones. 

2.  Add:    47 

63 


10     3  and  7  are  10,  or  1  ten. 
10       6  tens  and  4  tens  are  10  tens. 
110     10  tens  and  10  are  110. 


3.  Add: 

27G 
359 

15 
12 
5 

()35 

4. 

Add: 

427 

398 

15 
11 

i 

825 

5.  Add: 

32 

49 

76 

58 

85 

67 

94 

23 

88 

()3 

25 

72 

47 

5-: 

3(> 

99 

97 

S() 

78 

63 

5S 

47 

85 

46 

('»4 

57 

59 

8S 

94 

S7 

76 

76 

44 

54 

5 .5 

54 

143 

354 

145 

252 

32 

35 

34 

45 

342 

435 

514 

145 

45 

43 

25 

54 

235 

143 

152 

243 

92  THE   RATIONAL   ARITHMETIC. 

1.  A  farmer  kept  fifteen  sheep  in  one  field,  twenty-four 

in  another,  thirty-one  in  another,  and  forty-three 
in  another.  How  many  sheep  did  he  have  in  all 
the  fields? 

2.  George  earned  53  dollars  in  the  winter,  43  dollars 

in  the  spring,  25  dollars  in  the  summer,  and  34 
dollars  in  the  fall.  How  many  dollars  did  he 
earn  in  the  whole  year  ? 

3.  A  girl  paid  35  cents  for  a  book,  15  cents  for  paper, 

3  cents  for  a  ruler,  and  23  cents  for  a  box  of 
paints.     How  much  did  she  pay  for  all  ? 

4.  A  man  traveled  one  hundred  thirty -five  miles  the 
.     first  week,  two  hundred  fifty -four  miles  the  second 

week,  and  ^ve  hundred  forty -one  miles  the  third 
week.     How  far  did  he  travel  in  the  three  weeks  ? 

5.  I  paid  135  dollars  for  a  horse,  154  dollars  for  a  car- 

riage, and  23  dollars  for  a  harness.  How  much 
did  they  all  cost  me  ? 

6.  How  long  a  line  will  it  take  to  go  around  a  house 

that  is  thirty-six  feet  long  and  twenty-eight  feet 
wide  ? 

7.  A  man  had  16  dollars,  which  was  15  dollars  less 

than  he  needed  to  buy  a  suit  of  clothes.  What 
was  the  price  of  the  suit  ? 

8.  Arthur  earns  12  dollars  in  one  month  and  William 

10  dollars.  If  their  father  earns  as  much  as  both 
of  them  how  much  does  he  earn  ?  How  much  do 
the  three  earn  ? 

9.  Mr.  Stone  bought  a  lot  for  354  dollars.     He  built  a 

fence  around  it  at  a  cost  of  103  dollars.  What 
did  the  whole  cost? 


PART  FIRST. 

93 

1.  From 

43 

54   67   89 

354 

597 

728 

Take 

11 

21   34   45 

142 

423 

415 

32 

2.  Eeacl  25,  37,  and  78  as  follows: 

25  =  2  tens  and  5  ones.     (20+5.) 

1  ten  and  15  ones.     (10+15.) 
37  =  3  tens  and  7  ones.     (30  +  7.) 

2  tens  and  17  ones.     (20+17.) 
78  =  7  tens  and  8  ones.     (70+8.) 

6  tens  and  18  ones.     (60+18.) 

3.  Read  in  the  same  way  32,  46,  54,  48,  67,  34,  74. 

4.  From  72  take  35.  5  ones  cannot  be  taken  from  2 

72=60+12  ones.     Change  72  to  6  tens  and 

35=30+5  12  ones.     5  ones  from  12  ones  are 

30+  7  =  37  7;  3  tens  from  6  tens  are  3  tens. 

5.  From  92  take  44.  92  =  80  +  12 

44=40+  4 


40+  8=48 

~ 

(].  From 

131  take  43. 

131  = 

120+11 

43  = 

40+  3 

80+  8  = 

:88 

7.  Subtract: 

30 

40 

80 

32 

42 

53 

72 

61 

13 

15 

24 

13 

14 

24 

45 

22 

71 

94 

81 

91 

84 

62 

73 

82 

13 

45 

54 

45 

25 

33 

15 

54 

250 

361 

454 

583 

892 

951 

123 

143 

235 

354 

443 

243 

04  THE    RATIONAL   ARITHMETIC. 

1.  A  man  l;)oiTowed  73  dollars  and  returned  54  dollars. 

How  mucli  did  lie  still  owe  ? 

2.  In  the   morning  there  were  ninety -one  pounds  of 

sugar  in  a  barrel,  and  in  the  evening  there  wei*e 
forty -three  pounds.  How  many  j)ounds  had  been 
taken  out  during  the  day  ? 

3.  A  boy  earned  82  dollars  and  spent  25  dollars  for  a 

])icycle.     How  much  money  had  he  left? 

4.  One  book  contains  three  hundred  eighty -two  pages 

and  another  two  hundred  thirty-five  pages.  How 
many  more  pages  are  there  in  the  first  book  than 
in  the  second? 

5.  A  farmer  sold  a  horse  for  160  dollars,  which  was 

24  dollars  more  than  it  cost.  What  was  the  cost 
of  the  horse  ? 
C).  It  requires  ninety  feet  of  molding  to  go  around  a 
parlor  and  sixty-three  feet  to  go  around  a  din- 
ing-room. How  much  more  is  required  for  the 
parlor  than  for  the  dining-room?  Hoav  much  is 
required  for  both  rooms  ? 

7.  Clara's  j^urse  contains  ()3  cents.     If  she  spends  46 

cents  for  a  ])ook,  how^  much  money  Avill  there  1)6 
left? 

8.  In  one  school-room,  there  are  six  hundred  seventy- 

two  books;  in  another  school -room,  two  h und I'ed 
forty-three  books.  Hoav  man\'  more  l)ooks  in  the 
first  room  than  in  the  second  ? 
V).  A  cistern  that  will  hold  one  hundred  fifty-two 
barrels  of  water  has  only  forty-thi'ee  l)ai'r(ils  in  it. 
How  many  Larrels  of  water  will  1)0  i'e(|iiired  to 
fill  it? 


PART   FIRST.  95 

1.  Multiplication  is  tlie  addition  of  equal  numhers. 

2.  How  many  are  tAVO  47 ^s,  or  2  times  47  ? 

47  ■  47 

47  _2 

14        or       14     Two  7's  are  14,  or  1  ten  and  4  ones. 
8  8       Two  4  tens  are  8  tens. 

94  94     8  tens  and  14  are  94. 

3.  How  many  are  tliree  58's,  or  3  times  58? 

58 


58 

58 

58 

or 

3 

24 

24 

Tliree  8 

's  are 

24. 

15 

15 

Three  5 

tens 

are  15 

tens. 

174 

174 

15  tens  , 

and  2 

4  are 

174. 

4.  Multiply 
36 

• 
• 

28 

57 

38 

76 

41 

45 

79 

2 

3 

2 

4 

3 

5 

4 

2 

26 

89 

93 

88 

67 

80 

78 

90 

0 

4 

3 

2 

4 

3 

5 

4 

5.  HoAv  many  are  four  243 ^s,  or  4  times  243  ? 
243 


12     Four  3's  are  12. 
16       Four  times  4  tens  are  16  tens. 
8         Four  times  2  hundreds  are  8  hundreds. 

972  Adding,  6  tens  and  1  ten  are  7  tens,  8  hun- 
dreds  and  1  hundred  are  9  hundreds, 
making  972. 


96  THE   RATIONAL   ARITHMETIC. 


.  Multiply: 

325     438 

147 

235 

268 

470 

138     1G7    295 

3          2 

5 

4 

3 

2 

5         4         2 

179     489     249     304     169     230     294    157    109 
3  2         4         3  5  43         5         4 


2.  A    gardener   set    out    four    rows    of   trees,  putting 

eighty -two  trees  in  each  row.     How  many  trees 
(lid  he  set  out? 

3.  If  a  person  j^ays  4  dollars  a  Aveek  for  board,  how 

much  will  he  pay  in  a  year,  or  fifty-two  weeks? 

4.  There  are  twenty -four  sheets  of  paper  in  a  quire. 

How  many  sheets  are  there  in  five  quires  ? 

5.  How  many  bushels  of  wheat  are  there  in  ninety -six 

bags,  if  each  bag  contains  two  bushels  ? 

6.  What  will  three  pianos  cost  at  285  dollars  each? 

7.  A    family   uses   thirty-eight   quarts   of   milk    in  a 

month.     How  much  Avill  the  milk  l)ill  amount  to 
at  5  cents  a  ( pi  art? 

8.  There  are  one  hundred  ninety -six  pounds  of  flour  in 

a  barrel.     How  many  pounds  in  four  barrels? 

9.  Mr.  Gates  sold  his  horse  for  87  dollars.    I  sold  mine 

for  one -third  as  much.     How  much  did  I  receive 
for  my  horse  ? 

10.  If  Mr.  Field  pays  36  dollars  for  one  month's  rent, 

what  will  his  rent  be  for  five  months  ? 

11.  One   hundred  ninety -six   loaves    of   bread    can    be 

made  from  a  barrel  of  flour.     How  many  loaves 
can  be  made  from  five  barrels  of  flour  ? 

12.  Dr.  Allen  pays  75  dollars  a  year  for  his  telephone. 

What  will  it  cost  him  for  four  years  ? 


PART   FIRST. 


07 


1.  Whiitis  i  of  42? 

2)42     In  42  there  are  4  tens  and  2  ones. 
21         tens  is  2  tens;  i  of  2  ones  is  1. 

^  of  42  is  2  tens  and  1,  or  21. 

2.  Find: 

i  of  24    2)24 


Jr  of  4 


i  of  28     2)28       i  of  60    2)60 


i  of  36  3)36  1  of  63  3)63  i  of  39    3)39 

i  of  66  3)66  1  of  93  3)93  J  of  96    3)96 

i  of  48  4)48  i  of  84  4)84  i  of  44    4)44 

i  of  80  4)80  i  of  88  4)88  i  of  120  4)120 

-J  of  55  5)55  4  of  50  5)50  |  of  155  5)155 

3.  Kead  32,  54,  and  88  as  follows: 
32-=3  tens  and  2   (30  +  2). 
t    2  tens  and  12   (20+12). 

1  ten  and  22   (10  +  22). 
54  =  5  tens  and  4  (50+4). 

4  tens  and  14   (40+14). 

3  tens  and  24  (30+24). 

2  tens  and  34  (20+34). 

1  ten  and  44  (10+44). 
88  =  8  tens  and  8   (80+8). 

6  tens  and  28   (60+28) 

5  tens  and  38   (50+38) 

4  tens  and  48  (40+48) 

3  tens  and  58   (30+58) 

2  tens  and  68   (20+68) 
1  ten  and  78   (10+78). 


98  THE   RATIONAL   ARITHMETIC. 

1.  Read  in  as  many  ways  as  possible,  34,  56^  72,  46, 

68,  81,  96,  45,  and  115. 

2.  Wliat  is  one-lialf  of  tliirty-two  marbles? 

2 )82^20+12         We  cannot  find  i  of  3  tens  evenly. 
10-f   6  =  16      Change  32  to  2  tens  and  12. 

i  of  2  tens  is  1  ten;  ^  of  12  is  6. 

3.  A  boat  sailed  fifty -four  miles  in  two  hours;  how  far 

did  it  sail  in  one  hour? 
In  one  hour  it  sailed  |  of  54  miles. 
2)54^:40+14  Change  54  to  4  tens  and  14.     ^ 

20-h  7  =  27      of  4  tens  is  2  tens;  J  of  14  is  7. 

4.  Seventy -five  aj^ples  are  separated  into  three  equal 

piles.     How  many  aj)j)les  are  there  in  each  pile  ? 
In  each  pile  there  are  J  of  75  apples. 
3)75  =  60+15  Change  75  to  6  tens  and  15.    j. 

20+  5  =  25      of  6  tens  is  2  tens;  ^  of  15  is  5. 

-• 

5.  Find: 

i  of  98     2)98         -I  of  42     3)42         i  of  54     2)54 

i  of  51    3)51         i  of  92    4)92        |  of  75    5)75 
i  of  68    4)68         i  of  75    5)75         i  of  56    4  )56 

6.  Ninety-six  marbles  are  divided  equally  among  four 

boys.     How  many  marbles  has  each  boy  ? 

Each  boy  has  J  of  96  marbles. 

^J^'^^      Change  96  to  8  tens  and  16.     i  of  8  tens 

- —  is  2  tens;  1  of  16  is  4. 

24 


PART   FIRST.  99 

1.  There  are  one  liundred  fifteen  scholars  in  five  equal 
classes.  How  many  scliolars  are  there  in  each 
class  ? 

In  each  class  there  are  i  of  115  scholars. 
.xf-i^      Chano-e  115  to  10  tens  and  15.     \  of  10 
tens  is  2  tens;    I  of  15  is  8. 


28 

2.  There  are  one  hundred  forty -four  trees  in  four  equal 
rows.     How  many  trees  are  tliere  in  eacli  row? 
In  each  row  there  are  J  of  144  trees. 

tens  is  8  tens;   J  of  24  is  6. 


86 

8.  A  man  walks  three  miles  an  hour.     At  the  same 

rate,  how  many  hours  will  it  take  him  to  walk 

one  hundred  sixty-two  miles? 

It  will  take  as  many  hours  as  there  are  8's  in  162. 

ox^V^     Read  162  as  15  tens  and  12.     There  are 
8)lb2  ,    .  ^  ,    . 

50  8  s  m  15  tens;  there  are  4  8s  m  12. 


50  and  4  are  54. 
4.  Divide: 

2)178     8)171  4)172  5)175  2)866  4)896  5)150 

5)845     4)180  8)294  2)250  8)426  2)548  4)188 

8)678     5)470  2)478  4)272  5)215  8)519  2)672 

4)872     8)987  5)595  2)686  4)524  5)755  8)648 

4)886     5)485  2)946  8)819  4)296  5)875  8)201 


100  THE   RATIONAL   APaTHMETTC. 

1.  What  is  tlie  cost  of  one  lot,  if  tliree  lots  cost  516 

dollars  ? 

2.  A  farmer  has  three  hundred  fifteen  bushels  of  pota- 

toes.     If  he  puts  them  in  barrels,  each  holding 
three  bushels,  how  many  barrels  will  he  need? 

3.  A  steamboat  makes  a  trip  of  eight  hundred  forty- 

three  miles  in  tliree  days.     How  many  miles  does 
it  run  in  one  day  ? 

4.  A  clerk,  selling  cloth  at  2  dollars  a  yard,  received 

506  dollars  in  one  day.     How  many  yards  did  he 
sell? 

5.  How  many  gallons  in  seven  hundred  twenty-eight 

quarts  ? 

6.  A  dealer  bought  five  bicycles  for  225  dollars.    AVhat 

was  the  cost  of  one  bicycle? 

7.  If  a  man  saves  3  dollars  a  week,  how  many  weeks 

will  it  take  him  to  save  enough  money  to  pay  for 
his  house,  on  which  he  owes  879  dollars? 

8.  A  farmer  who  has  four  hundred    ninety-six  acres 

of  land,  divides  it  into  four  farms  of  equal  size. 
What  is  the  size  of  each  farm  ? 

9.  A  carjDenter  receives  160  dollars  for  building  five 

rods  of  fence.     What  was  the  cost  per  rod  ? 

10.  There  are  three  hundred  sixty -five  days  in  one  year. 

How  many  days  in  one -fifth  of  a  year? 

11.  A  gardener  has  eight  hundred  twenty -eight  ]3ounds 

of   seed,   which  he  puts  into  four-pound   sacks. 
How  many  sacks  will  be  required  ? 

12.  In  going  to  school  and  returning  home,  Henry  has 

to  walk  nine  hundred  seventy -eight  yards.     How 
far  does  he  live  from  the  school  house  ? 


•>  ■>       >       >    > 


PAET   SECOND. 


A 


B 


D 


1.  The  above  is  the  plan  of  a  lot  drawn  to  the  scale,  1  iuch 

to  12  feet.      This  means  that  an  inch  in  length  in  the 
drawing  represents  12  feet  in  any  line  in  the  lot. 

2.  How  many  feet  is  it  from  A  to  B? 

3.  How  many  feet  is  it  from  A  to  F? 

4.  How  many  feet  is  it  from  F  to  E  ?    From  D  to  E  ?    From 

B  to  C  ?     From  C  to  D  ?     From  A  through  B  to  C  ? 
From  A  through  F  to  E? 

5.  How  many  feet  of  fence  are  required  to  fence  the  lot? 

6.  There  are  3  feet  in  a  yard,  how  many  yards  from  A  to  F:^ 

From  A  to  B?     How  many  yards  around  the  lot? 

101 


Kk':  THE   RATIONAL   ARITHMETIC. 

1.  I£.tli0  lot  veie  square  with  sides  the  length  of  A  to  F, 

how  many  yards  around  it?  If  square  with  sides  the 
length  of  A  to  B,  how  many  yards  around  it  ?  If  square 
with  sides  the  length  of  B  to  C,  how  many  yards 
around  it? 

2.  Taking  steps  2  feet  long,  how  many  steps  would  one  take 

in  walking  once  around  the  lot  described  on  page  101? 

3.  How  many  such  steps  would  he  take  in  walking  halfway 

around  the  lot?     In  walking  twice  around  the  lot? 

4.  A  car  is  61  feet  long,  how  long  is  a  train  of  1  such  cars  ? 

Of  5  such  cars? 

5.  A  block  is  453  feet  long.     A  lamp-post  is  236  feet  from 

one  end  of  the  block;  how  far  is  it  from  the  other  end? 

6.  A  strip  of  wood  6  yards  long  is  cut  into  pieces  2  feet 

long.      How  many  pieces  are  there? 

7.  A  girl  rolled  a  hoop  12  yards  at  one  time  and  16  yards 

another  time.  How  many  yards  did  she  roll  it  in  all? 
How  many  feet? 

8.  A  house  is  54  feet  high  and  a  flag  pole  on  top  of  the  house 

is  24  feet  high.  How  many  feet  from  the  ground  to 
the  top  of  the  flag  pole?     How  many  yards? 

9.  A  field  is  240  feet  wide,  and  325  feet  long.     How  many 

feet  around  it? 
10.  A  block  is  486  feet  long,  and  273  feet  wide.     What  is  the 

difference  between  the  length  and  the  width  in  feet? 

In  yards? 
11„  A  boy  lives  624  feet  from  the  store.     In  going  to  the 

store  and  returning,  hoAv  many  feet  will  he  walk  ?     How 

many  yards?     If  he  goes  to  the  store  and  returns  once 

a  day,  4  days  in  the  week,  how  many  yards  will  he  walk? 
12.   A  rail  in  the  street  car  track  is  10  yards  long.    How  many 

rails  in  50  yards  of  a  single  rail  of  track?    In  2  rails  of 

track?     In  all  the  rails  of  2  tracks? 


PART   SECOND. 


103 


27  ft 

ZIFT 
DINING  ROOM          ^ 

H 

0-'                    PAP  LOP 

•  1 

KITCMEN             ^ 

-n 
H 

rx3              5iTTIMG   POOh 

T] 

H 

1.  The  above  plan  is  for  tbe  lower  story  of  a  house. 

2.  Howmany  yards  long  is  the  parlor?  Sitting-room?  Dining- 

room  ?     Kitchen  ?     How  many  yards  wide  is  each  room  ? 

3.  How  many  feel  of  mokling  will  reach  around  each  room? 

How  many  yards? 
4:.   How  many   feet   of   molding   will   reach   around   all    the 

rooms?     How  many  yards? 
5.   How  many  strips  of  carpet,  1  yard  wide,  will  cover  the 

parlor  floor  ?     How  many  yards  long  will  each  strip  be  ? 

How  many  yards  in  all  the  pieces  for  the  parlor  floor? 
f).   How  many  strips  of  carpet,  I  yard  wide,  will  cover  the 

sitting-room  floor?     How  many  yards  in  all  the  carpet 

for  the  sittinsf-room  ? 

7.  How  many  strips,   1    yard    wide,  will    cover  the  dining- 

room  floor?     How  many  yards  in  all  the  carpet  for  the 
dinino:-room? 

8.  How    many    yards    will    be    required    for    the    3    rooms 

together  ? 


104  THE   RATIONAL   ARITHMETIC. 

1.  Joe  and  Harry  live  20  yards  apart.      How  many  feet  of 

telephone  wire  do  they  need  to  connect  the  2  houses, 
allowing  2  yards  for  connection  at  the  ends? 

2.  The  blackboard  in  the    schoolroom   is  24  feet  long.      It 

is  divided  into  sections  24  inches  wide,  how  many  sec- 
tions are  there?  If  there  were  42  feet  of  blackboard, 
how  many  such  sections  would  there  be? 

3.  How  many  yards  of  border  will  be  required  to  go  around 

the  walls  of  a  parlor  which  is  15  feet  by  18  feet? 
Around  a  bedroom  which  is  12  feet  by  15  feet? 

4.  I  Avished  to  carpet  my  stairs,  and  found  I  needed  for  that 

purpose  12  yards.  It  takes  18  inches  for  each  step. 
How  many  steps  are  there  in  the  staircase? 

5.  Mr.  Benton  had  4  book  shelves  which  are  3  feet  long. 

The  first  shelf  he  filled  with  books  4  inches  thick.     How 

many  books  did  he  put  on  the  shelf? 
The  second   shelf    he    filled  with  books    3  inches  thick. 

How  many  were  there? 
The  third  shelf  he  filled  with  books  2  inches  thick.     How 

many  were  there? 
The  fourth  shelf,  he  filled  with  books  1  inch  thick.     How 

many   did  he  put  on   the   fourth   shelf?      How   many 

books  did  he  put  on  all  the  book-shelves? 
0.   Harold  is  3  feet  9  inches  tall  and  James  is  4  feet  tall. 

What  is  the  sum  of  their  heights? 

7.  George  is  4  feet  9  inches  tall  and  John  is  3  feet  3  inches 

tall;  how  much  taller  is  George  than  John?  AVhat  is 
the  sum  of  their  heights? 

8.  James  is  3   feet  114^  inches  tall    and  Jessie  is   3  feet   7 

inches  tall;  what  is  the  difference  in  their  height? 

9.  A  room  is  9  feet  8  inches  high.      The  mantel  is  4  feet  6 

inches  from  the  floor.  How  far  is  it  from  the  mantel 
to  the  ceiling? 


PART   SECOND. 


105 


D 


M 


H 


K 


1.  Tliis  plan  of  a  building  is  drawn  to  the  scale  of  one  inch 

to  twelve  feet. 

2.  How  many  feet  is  it  from  A  to  B  ?     From  B  to  D  through 

C  ?     From  D  to  F  through  E  ?     From  F  to  H  through 
G  ?     From  H  to  M  through  K  and  L  ? 

3.  How  many  yards  is   it   from   P   to  O?     From  P  to  A? 

From  D  to  E  ?     From  G  to  K  through  H  ?     From  F  to 
L  through  G,  H,  and  K? 

4.  How  many  yards  is  it  from  C  to  N  through  B,  A,  P  and  O  ? 

5.  How  many  yards  is  it    from  N  to  G  through  M,  L,  K, 

and  H  ? 

6.  How  many  yards  is  it  from  G  to  C  through  F,  E,  and  D? 

7.  How  many  yards  is  it  around  the  entire  building? 

8.  How  many  feet  is  it  from   B  to  O,  following  the  dotted 

line?     HoAv  many  yards  is  it? 


106 


THE   RATIONAL   ARITHMETIC. 


A 


1 

1 

n 

U 

f- 

i 

1 

J 

o 

U 

— 

r^ 

La 

i^ 

\\ 

p\ 

U 

1  1 

^ 

1  1 

1 

L 

— 

1.  A  is  6.      How  many  6's  in  B?     How  many  in  C?     In  D? 

E?     F?     G?     H?     I?     J?     K?     L? 

2.  A  equals  (3,  B  equals  12.      To  what  is  C  equal?     D? 

F?     G?     H?     I?     J?     K?     L? 

3.  A  equals  wliat  part  of  B  ?     What  part  of  C  ? 
4   6  is  what  part  of  12?     What  part  of  18? 

36?     42?     48?     54?     60?     m?     72? 
5.   B  equals  how  many  A's?     What  part  of  C? 
F?     G?     H?     I?     J?     K?     L? 


Of  D? 

Of  24? 


E? 

E? 

30? 


OfD?     E? 


PART   SECOND. 


107 


1.  12  is  how  many  6's?     What  part  of  18?     Of  24?     30? 

36?     42?     48?     54?     60?     66?     72? 

2.  C  equals  how  many  A's?     How  many  B's?     AVhat  part 

ofD?     OfE?     F?     G?     H?     I?     J?     K?     L? 

3.  18   is  how  many  6's?     How  many  12's?     What  part  of 

24?     30?     36?     42?     48?     54?     60?     66?     72? 

4.  D  equals  how  many  A's?     How  many  B's?     How  many 

C's?     What  part  of  E?      Of  F?      G?      H?      I?     J? 

5.  24  is  how  many  6's?     How  many  12's?     How  many  18's? 

What  part  of  30  ?     36?     42?     48?     54?     60?     72? 

6.  E  equals  how  many  A's?     How  many  B's?     How  many 

C's?     How  many  D's?     AVliat  part  of  F ?     Of  G?     H? 

7.  30  is  how  many  6's?     How  many  12's?    How  many  18's? 

How   many   24's?     What    part  of    36?     Of  42?     48? 

8.  F  equals  how  many  A's?     B's?    C's?     D's?    E's?     Etc. 


2 

12 

22 

32 

6 

42 

52 

62 

72 

6 

16 

26 

36 

6 

48 

56 

66 

76 

O 

13 

23 

33 

6 

43 

53 

63 

73 

7 

17 

27 

37 

6 

47 

57 

67 

77 

4 

14 

24 

34 

6 

44 

54 

64 

74 

8 

18 

28 

38 

6 

48 

58 

68 

78 

5 

15 

25 

35 

6 

45 

55 

65 

75 

9 

19 

29 

39 

6 

49 

59 

69 

79 

Add  the  red  figure  to  each  number  in  the  same  large  square. 

Subtract  it  from  each  larger  number.     Multiply  and  divide  in 

the  same  way. 

Note. — Have  pupils  construct  drill  tables  similar  to  those  on  pages  66 
and  67,  for  this  and  following  multiplication  tables,  pages  117,  ]25,  135,  143, 
149  and  153. 


108  THE   RATIONAL   ARITHMETIC. 

1.  Add  upward,  downward,  by  lines  to  the  right  and  to  the 
left: 


6 

6 

6 

3 

6 

6 

2 

3 

6 

2 

1 

6 

4 

2 

6 

6 

6 

6 

6 

1 

6 

1 

6 

() 

6 

6 

6 

6 

6 

6 

5 

6 

6 

6 

6 

6 

6 

6 

4 

1 

1 

3 

4 

5 

2 

6 

6 

5 

2.   Add,  subtract  and  multiply 


12 

18 

24 

30      36      42      48      54      60 

66 

72 

6 

6 

6 

6        6        6        6        6        6 

6 

i; 

13 

25 

37 

49       51       63       75       87 

99 

KH. 

6 

() 

6 

6         6         6         ()         6 

6 

r, 

3.  Divide: 

6)12       6)30       6)42  6)54       6)72       6V)^       6)48' 

^)i?       ^)^      ^1^  ^^)^      ^'M      ^)1?5      ^'H^    i 

4.  12  equals  how  many  6's?  36  equals  how  many  6's? 
24  equals  how  many  6'sV  42  equals  how  many  6's? 
48  equals  how  many  6's?  66  equals  how  many  6's? 
18  equals  how  many  6's?  30  equals  how  many  ()'s? 
54  equals  how  many  6's?  72  equals  how  many  6's? 

6  is  \  of 

6  is  I   of 

6  is  4f  of _. 

6  is   J   of 

6  is  tV  of __• 


.   6  is 

1 

3 

of 

6  is 

1 

of 

6  is 

1 

of 

6  is 

1 

of 

6  is 

1 
10 

of 

PART   SECOND.  100 


1.  3  is  I  of 7  is  «  of 


5  is  I  of  . _.  8  is  J  of  — 

2  is  J  of 9  is  I  of  __ 

4  is  ^  of 6  is  I  of  . — 

10  is  ^  of 12  is  -I  of  _ 


2.  How  many  6's  are  there  in  13?  In  32? 
How  many  6's  are  there  in  57?  In  51? 
How  many  O's  are  there  in  25  ?  In  45  ? 
How  many  6's  are  there  in  22?  In  40? 
How  many  6's  are  there  in  75?     In  63? 

The- sign  for  dollars  is  $;   (>  dollars  is  written  $6. 
The  sign  for  cents  is  ^;  25  cents  is  Avritten  25^. 

3.  At  $6   a  cord  what  is  the  cost  of  5  cords  of   wood?     7 

cords?     9  cords?     11  cords? 

4.  Six  windows  contain  48  panes  of  glass.     How  many  panes 

are  there  in  each  window?     In  one-half  of  one  window? 

5.  How  many  minutes  are  there  in  an  hour?     What  part  of 

an  hour  are  10  minutes?     20  minutes?     30  minutes? 
40  minutes? 

6.  One  man  built  a  fence  in  60  days.      How  many  men  could 

have  built  it  in  6  days  ?     In  5  days  ?     In  3  days  ? 

7.  One  yard  of  braid  is  worth  6^,  how  much  are  5  yards  worth  ? 

8.  At  $6  a  barrel,  how  many  barrels  of  flour  can  be  bought 

for  $72?     For  $54?     For  $36?     For  $18?     For  $48? 
For  $12? 

9.  In  an  orchard  there  are  54  trees  in  six  equal  rows.     How 

many  trees  are  there  in  one  row? 

10.  Joe  went    to  the  store  with  36^  and    spent    all    but  6^. 

What  part  of  his  money  did  he  have  left?     How  much 
had  he  left  ? 

11.  In  going  to  school  a  boy  rides  24  blocks  and  walks  one- 

sixth  as  far  as  he  rides.      How  many  blocks  does  he 
walk  ?     How  far  does  he  travel  ? 


no  THE   RATIONAL   ARITHMETIC. 

1.  Tlie  height  of  a  tree  is  72  feet,  which  is  6  times  the  dis- 

tance around  it  at  the  ground.  How  many  feet  around 
it  at  the  ground? 

2.  If  I  buy  5  eight-cent  postage  stamps  and  give  $1  in  pay- 

ment, how  much  change  should  I  receive? 

3.  Charles  traveled  87   miles  on  his  wheel  in  3  days.      At 

the  same  rate  how  far  can  he  go  in  5  days?     In  6  days? 

4.  In  one  field  a  farmer  has  96  sheep,  which  are  one-sixth  of 

his  entire  flock.      How  many  sheep  has  he? 

5.  If  $120  were  divided  equally  among  6   men,  how  much 

money  would  each  one  receive?  How  much  would  2 
receive  together?     3  together? 

6.  A  piece  of  cloth  is  54:   yards  long.      One-sixth  of  it  was 

sold  at  $2  a  yard.  How  much  was  received  from  the 
sale?  How  much  of  the  piece  was  left?  How  rnucli 
was  it  worth  at  the  same  rate? 

7.  If  a  man  earns  $71  a  month  and  spends  $52  a  month,  how 

much  will  he  save  in  that  time?  How  much  will  he 
save  in  0  months? 

8.  How  many  hours  are  there  in  1  day  ?     In  one-half  a  day  ? 

In  one-sixth  of  a  day  ?  How  many  hours  are  there  in 
6  days? 

9.  A  barrel  holds  31|^  gallons  ;  how  many  gallons  will  6  bar- 

rels hold? 

10.  A  farmer  owned  486  acres  of  pasture  land.     He  bought 

one-sixth  as  many  acres  more.  How  many  acres  did 
he  buy  ?     How  many  acres  did  he  then  own  ? 

11.  A  mile  from  north  to  south  is  8  blocks,  and  from  east  to 

west  13  blocks.  How  many  blocks  will  a  boy  travel  in 
going  6  miles  north  and  6  miles  west? 

12.  What  is  the  cost  of  27  yards  of  sewer  pipe  at  $2  a  foot? 

13.  How  many  weeks  will  it  take  a  man  to  save  $297  if  he 

saves  $3  each  week? 


FART   SECOND.  Ill 

1.  How  many  square  inclies  in  a  rectangle  that  is  6  inclieh-- 

long  and  S  inches  wide?  (See  page  54.)  One  that  is 
0  inches  long  and  (j  inches  wide?  One  that  is  0  inches 
long  and  8  inches  wide  ?  One  that  is  6  inches  long  and 
12  inches  wide? 

2.  How  many  square  inches  in  a  G  inch  square?     Draw  one. 
8.  A  2  inch  square  equals  what  part  of  a  6  inch  square? 

4.  A  3  inch  square  equals  what  part  of  a  G  inch  square? 

5.  How  many  4  inch  squares  in  a  G  inch  square? 
G.   How  many  5  inch  squares  in  a  6  inch  square  ? 

7.  A  4  inch  square  equals  what  part  of  a  G  inch  square? 

8.  A  5  inch  square  equals  what  part  of  a  6  inch  square? 

9.  To  what  are  3  feet  in  length  equal? 

10.  WJiat  then  may  we  call  a  figure  3  feet  square? 

11.  On  page  50  suppose  each  small  square  in  the  yellow  fig- 

ure were  one  foot  long.  How  long  would  the  yellow 
figure  then  be?  How  wide?  How  many  square  feet 
Avould  it  contain?  How  many  square  yards?  How 
many  feet  in  the  perimeter  of  a  square  yard? 

12.  On  page  54    suppose    each   small    square  were  one  foot 

square.  Hoav  wide  would  the  figure  be?  How  long? 
How  many  square  feet  Avould  it  contain  ? 

13.  How    many  square    yards  in   a  figure    2    yards  square? 

How  many  feet  long  is  one  side  of  such  a  figure  ?  How 
many  square  feet  does  such  a  figure  contain  ? 

14.  How  many   square   feet   in   3   square  yards?       5   square 

yards?     (>  square  yards? 

15.  How  many  square  yards  in   18   square  feet?     3G  square 

feet  ?  27  square  feet  ?  54  square  feet  ?  45  square  feet  ? 
IG.  Turn  again  to  the  yellow  figure  on  page  50.  Suppose  each 
side  is  one  yard  long.  What  part  of  a  square  yard  is 
3  square  feet?  1  square  foot?  G  square  feet?  2 
square  feet?     5  square  feet?     4  square  feet? 


112 


THE   RATIONAL   ARITHMETIC. 


A 


1            ^           ' 

/           j                         1    ^\ 

1.  How  long  is  the  box  A? 
inches  in  one  side? 


How  deep?     How  many  square 


' 


PART   SECOND.  113 

1.  B  is  a  piece  of  paper  the  size  from  which  to  cut  such  a 

box  without  a  cover. 

2.  How  long  is  this  paper?     How  wide  is  it? 

3.  The   paper  is   then  a   rectangle   of inches  by 

inches. 

4.  What  is  the  area  of  this  paper? 

5.  A  box  is  2  inches  long,  2  inches  wide  and  2  inches  high. 

How  many  square  inches  in  the  sides  and  bottom  of 
the  box? 

6.  What  are  the  dimensions  of  the  piece  of  paper  necessary 

to  make  it?     What  is  its  area? 

7.  What  are  the  dimensions  of  the  piece  of  paper  necessary 

to  make  a  box  3  inches  long,  3  inches  wide  and  3  inches 
high,  without  a  cover?     What  is  the  area  of  the  paper? 

8.  What  are  the  dimensions  of  a  box  that  can  be  made  from 

a  piece  of  paper  12  inches  long  and  12  inches  wide, 
without  a  cover? 

9.  A  box  is  4  inches  long,  3  inches  wide  and  2  inches  high. 

How  large  must  the  paper  be  in  order  to  make  it  with- 
out a  cover?  How  many  square  inches  of  paper  are 
necessary  ? 

10.  What  are  the  dimensions  of  the  piece  of  leather  necessary 

to  line  a  box  that  is  6  inches  long,  2  inches  wide  and 
2  inches  high,  without  a  cover?  How  many  square 
inches?  What  will  the  leather  for  such  a  box  cost  at 
6  cents  a  square  inch? 

11.  How  many  square  feet  of  cloth  are  needed  to  line  a  box  6 

feet  long,  3  feet  wide  and  2  feet  high,  with  a  cover? 

12.  The  length  of  a  room  is  6  yards,  its  height  4  yards.    How 

many  square  yards  in  one  side  of  the  room?  In  the  2 
sides?  The  room  is  5  yards  wide,  what  is  the  area  of 
one  end  wall?  Of  both?  Of  the  ceiling?  Of  the 
floor?     Of  the  entire  inside  surface  of  the  room? 


114 


THE   RATIONAL   ARITHMETIC. 


I 
X 

1 

• 

rrr 

■■ 

ZF 

a 

Y 

b 

e 

I 


PART   SECOND.  11.3 

1.  The  figure  X  is  enclosed  by  the  black  irregular  line.     It 

is  cut  into  four  rectangles  by  the  dotted  lines.  These 
rectangles  are  marked  I,  II,  III,  lY. 

2.  Measure  the  length   and  width  of  I.      What  is  its  area? 

AV^iiat  are  the  dimensions  of  II?  Its  area?  Dimen- 
sions of  III?  Its  area?  Dimensions  of  IV?  Its 
area  ? 

3.  Now  what  is  the  area  of  the  figure  X?     into  what  other 

rectangles  might  X  bo  cut  t(j  find  its  area?  What  is 
the  perimeter  of  X? 

4.  What  part  of   the   rectangle   I   equals  II?      III?      IV? 

What  part  of  II  equals  IV  ?     Ill  ? 

5.  Suppose  each  inch  in  the  dimensions  of  the  figure  X  rep- 

resented 3  feei  What  would  be  the  width  of  the 
rectangle  I?  Its  length?  How  many  square  feet 
would  it  contain?  How  many  square  yards? 
(j.  What  would  then  be  the  dimensions  of  II?  Its  area? 
Dimensions  of  III?  Its  area?  Dimensions  of  IV? 
Its  area? 

7.  If  I=S.  what  is  II?     III?     IV? 
If  11-36,  what  is  IV ?     Ill ?      I ? 

8.  The  figure  Y  is  made  up  of  the  rectangles  c/,  h,  c. 
[).   H-ow  long  is  a?     How  wide?     What  is  its  area? 

ID.   What  are  the  dimensions  of  h?     Its   area?     Dimensions 
of  c?     Its  area? 
P*  11.   What  is  the  area  of  the  figure  Y?     Is  there  more  than 
one  way  to  find  the  area  of  Y? 

12.  Suppose  each  inch  in  the  dimensions  of  the  figure  Y  rep- 

resented 3  feet.  What  would  l^e  the  area  of  af  !>?  cf 
AVliat  would  be  the  area  of  the  entire  surface  of  Y  in 
square  feet?     In  square  yards? 

13.  What  is  the  area  of  X  and  Y  together,  in  square  feet  ?    In 

square  yards? 


nc 


THE   RATIONAL   ARITHMETIC. 


At 

E 

— I 


n 

U 

r 

1 

1 

J 

G 


K 


Pi 

D 

1  1 

1  1 

1 

l_ 

1.  A  is  7.     How  many  7's  in  B?     How  many  in  C?     In  D? 

E?     F?     G?     H?     I?     J?     K?     L? 

2.  A  equals  7,  B  equals  14.     To  what  is  C  equal?     D?     E? 

F?     G?     H?     I?     J?     K?     L? 
8.  A  equals  what  part  of  B  ?     What  part  of  C  ?     Of  D  ?     E  ? 
F?     G?     H?     I?     J?     K?     L? 

4.  7  is  what  part  of  14?     What  part  of  21?     Of  28?     35? 

42?     49?     56?     63?     70?     77?     84? 

5.  B  equals  how  many  A's?     What  part  of  0?     Of  D?     E? 

F?     G?     H?     I?     J?     K?    L? 

6.  14  is  how  many  7's?     What  paj-t  of  21?     Of  28?     35? 

42?     49?     56?     63?     70?     77?     84? 


PART   SECOND. 


117 


1.  C  equals  how  many  A's?     How  many  B's?     What  part 

o£D?     0£E?     F?     G?     H?     I?     J?      K?     L? 

2.  21  is  how  many  7's?    How  many  14's?    What  part  of  2S? 

Of  35?     42?     49?     56?     63?     70?     77?     84? 

3.  D  equals  how  many  A's?     How  many  B's?     How  many 

C's?    What  part  of  E?    OfF?    G?    H?    I?    J?    K?    L? 

4.  28  is  how  many  7's?     How  many  14's?     How  many  21's? 

What  part  of  35  ?     Of  42?     49?    56?     63?     70?     77? 

5.  E  equals  how  many  A's?     How  many  B's?     How  many 

C's  ?     How  many  D's  ?     What  part  of  F  ?     Of  G  ?     H  ? 
I?     J?     K?     L? 

6.  35  is  how  many  7's?     How  many  14's?     How  many  21's? 

How  many   28's?     What  part  of  42?      Of  49?     56? 
63?    70?     77?     84? 

7.  F  equals  how  many  A's?     How  many  B's?     C's?     D's? 

E's?     What  part  of  G?     Of  H?     I?     J?     K?     L? 

8.  42  is  how  many  7's?    How  many  14's?    How  many  21's? 

How  many  28's?     Etc. 


2 

12 

22 

32 

7 

42 

52 

62 

72 

6 

16 

26 

36 

7 

46 

56 

66 

76 

3 

13 

23 

33 

7 

43 

53 

63 

73 

7 

17 

27 

37 

7 

47 

57 

67 

77 

4 

14 

24 

34 

7 

44 

54 

64 

74, 

8 

18 

28 

38 

7 

48 

58 

68 

78 

5 

15 

25 

35 

7 

45 

55 

65 

75 

9 

19 

29 

39 

7 

49 

59 

69 

79 

Add  the  red  figure  to  each  number  in  the  same  large 
square.  Subtract  it  from  each  number  larger  than  itself. 
Multiply  and  divide  in  the  same  way. 


118  THE   RATIONAL   ARITHMETIC. 

1.   Add  upward,  downward,  by  lines  to  the  right  and  to  the 
left : 


7 

7 

6 

4 

5 

3 

2 

7 

7 

1 

2 

4 

() 

7 

7 

5 

G 

7 

3 

7 

0 

4 

7 

4 

7 

7 

7 

(> 

7 

5 

7 

6 

6 

4 

7 

7 

6 

7 

7 

7 

6 

6 

4 

3 

7 

1 

3 

3 

2 

2 

7 

4 

7 

2.   Add,  subtract  and  multiply: 


14 

28 

5G 

21   42 

84  35 

70 

63   78   59 

7 

r- 
< 

7 

7    7 

7   7 

7 

7   7   7 

83 

<0 

94 

67   77 

89   48 

99  132  576 

7 

7 

7 

7    7 

7 

r- 

7    7    7 

3.  Divide: 

7)14 

7)28 

7)42 

7)21 

7)56    7)70 

7)35 

7)49 

7)68 

7)84 

7)77    6)72 

4.  14  equals  how  many  7's?  42  equals  how  many  7's? 
28  equals  how  many  7's?  49  equals  how  many  7's? 
56  equals  how  many  7's?  21  equals  how  many  7's? 
35  equals  how  many  T's?  77  equals  how  many  7's? 
63  equals  how  many  7'sV  84  equals  hoAV  many  7'sV 

5.  7  is   ^5   of .  7  is   \  of 


7  is  \  of ..  7  is  \  of 

7  is  \  of 7  is  -^  of 


TAKT   SECOND.  n'.) 


7  is 

1 

2~ 

of 

7  is 

I   1 

of 

7  is 

1 
12 

> 

ot 

4  is 

1 

8 

of 

(•>  is 

1 

of 

8  is 

1 

T 

of 

0  is 

1 

5: 

of 

7  is 

1 

9 

of 

7  is 

1 

1  t) 

of 

6  is 

1 

of 

7  is 

1 

1 

of 

4  is 

1 

of 

Ois 

1 
3 

of 

11  is 

1  . 

'  of 

111  29  ? 

Ill  45? 

In  25  ? 

Ill  48? 

Ill  78? 

Ill  82  ? 

2.  How  many  7's  are  there  in  15? 
How  many  7's  are  there  in  37? 
How  many  7\s  are  there  in  50? 
How  many  7's  are  there  in  57? 
How  many  7's  are  there  in  8B? 
How  many  7's  are  there  in  73  ? 

3.  One  man  digs  27  feet  of  ditch;  another  17  feet,  and  a  boy 

7  feet.     How  many  feet  do  all  dig? 

4.  On  one  farm  there  are  754  feet  of  fence;  on  another  577 

feet.     How  much  more  fence  is  there  on  the  first  farm 
than  on  the  second? 

5.  A  grain  dealer  bought  378  bushels  of  wheat  in  one  place 

and  747  bushels  in  another.        He  sold   707  bushels; 
how  many  bushels  had  he  left? 
0.  A  man  bought  7  horses  at  $65  apiece;  how  much  did  he 
pay  for  all? 

7.  A  train  travels  252   miles  in  7  hours;  how  far  does  it  go 

in  1  hour? 

8.  If  14  pails  of  butter  weigh  42  pounds,  what  do  2  pails  of 

the  same  size  weisrh? 

9.  In  making  a  well,  63  feet  deep,  14  feet  were  dug  through 

clay.     If  '}j  of  the  well  was  dug  each  day,  how  many 
days  were  spent  in  digging  through  the  clay  ? 
10.  A  farmer  made  a  wire  fence  14  yards  long,  he  put  in  posts 
7  feet  apart,  and  7  rows  of  -wire.      How  many  posts  were 
there?     How  many  yards  of  wire  did  he  use? 


120 


THE   RATIONAL   ARITHMETIC. 


PART   SECOND.  121 

1.  The  lower  side  upon  which  a  triangle  rests  is  called  its 

base.     The  vertical  side  is  called  its  height,  or  altitude. 

2.  What  is  the  length  of  the  base  of  the  triangle  A  on  the 

opposite  page?     What  is  the  altitude? 

3.  Find  the  middle  point  of  the  altitude  and  the  middle 

point  of  the  long  side  of  the  triangle,  and  between 
these  two  points  suppose  the  triangle  cut  and  the 
upper  part  turned  about  to  the  side  of  A,  as  in  B. 

4.  What  do  we   call   the  figure   B?     What   is   its   length? 

What  is  its  width?     What  is  the  area  of  B? 

5.  What  then  is  the  area  of  the  triangle  A  ? 

6.  Cut  a  4-inch  square.     Draw  a  line  between  two  opposite 

corners,  and  on  this  line  cut  the  square  in  two.  What 
is  the  altitude  of  one  of  the  triangles  thus  formed? 
Its  base?     Find  its  area. 

7.  What  are  the  dimensions  of  the  triangle  C?     Draw  a  line 

from  the  center  of  the  base  to  the  center  of  the  angle 
opposite.  Suppose  the  left  side  of  the  triangle  C  to  be 
turned  about  and  laid  upon  the  longest  side  of  C  as  in 
the  figure  D.     What  is  the  figure  D  ? 

8.  What  are  the  dimensions  of  D  ?     What  is  its  area  ? 

9.  What  then  is  the  area  of  the  triangle  C  ? 

10.  Suppose  the  base  of  the  triangle  C  were  6  feet  and  its 

altitude  6  feet,  what  would  be  the  area  of  the  triangle? 

11.  The  area  of  such  a  triangle  as  C  may  be  found  in  another 

way,  as  in  the  triangle  E. 

12.  Find  the  middle  point  of  the  sides  of  the  triangle,  and 

suppose  the  triangle  to  be  cut  at  these  points  and  the 
top  part  equally  divided  and  placed  on  the  sides  of  the 
lower  part  of  the  triangle,  as  in  the  figure  F.  What 
figure  do  we  then  have?  What  are  its  dimensions? 
AVliat  is  its  area? 

13.  What  then  is  the  area  of  the  triangle  E? 


122  THE    RATIONAL   ARITHMETIC. 

1.  Draw  the  following  9  triangles  and  find  the  area  of  each: 
The  base  is  (5  inches  and  the  altitude  4  inches. 

The  l)ase  is  8  inches  and  the  altitude  6  inches. 
The  base  is  9  inches  and  the  altitude  4  inches. 
The  base  is  5  inches  and  the  altitude  8  inches. 
The  l)ase  is  12  inches  and  the  altitude  10  inches. 
The  base  is  J 1  inches  and  the  altitude  14  inches. 
The  base  is  18  inches  and  the  altitude  12  inched. 
The  base  is  1^3  inches  and  the  altitude  10  inches. 
The  base  is  15  inches  and  the  altitude  14  inches. 

2.  A  car  contains  1)  seats,  each  of   which  holds  7   persons. 

Ht)W  many  persons  can  be  seated  in  the  car? 
8,   There  are  3  cars  of  this  size  in  a  train.     How  many  per- 
sons can  be  seated  in  the  train? 

4.  In  front  of  a  house  there   are   25   feet   of  sidewalk  7  feet 

wide.      How  many  square  feet  in  the  sidewalk? 

5.  A  door  is  7  feet  high  and  8  feet  wide.     How  many  scj^uare 

feet  in  the  door?  How  many  square  feet  if  the  door 
were  3^  feet  Avide? 

6.  How  many  books  would  there  ])e  in  a  bookcase  containing 

7  shelves,  if  there  were  12  books  on  each  shelf?  11  on 
each  shelf?  9  on  each  shelf?  10  on  each  shelf? 
20  on  each  shelf?     30  on  each  shelf? 

7.  A  table  is  7  feet  long  and  4  feet  wide.    What  is  its  perim- 

eter?    What  is  its  area? 

8.  There  are  35  pupils  enrolled  iii  one  schoolroom.     If  5  are 

away,  how  many  are  present?  What  part  of  the  whole 
number  is  absent?  What  part  of  the  whole  number  is 
present  ? 

9.  A  fruit  dealer  sells  pineapples  at  34  cents  apiece.      How 

much  money  will  he  receive  for  7  pineapples? 
10.   If  I  save  57  dollars  a  month  for  7  months,  how  much 
more  must  I  save  to  have  $700? 


PART    SECOND.  1-23 

1.  A  piece  of  pipe  is  80  feet  long.      How  long  are  7  such 

pieces  together? 

2.  In  a  cellar  there  are  4  bins,  each  holding  7  bushels.      How 

many  sacks  of  apples,  each  holding  2  bushels,  will  be 
required  to  fill  the  bins? 

3.  The  distance  around  a  field  is  63  rods.      \  of  the  fencing 

around  it  is  hedge,  the  remainder  is  board  fence.    How 
many  rods  of  hedge?     How  many  rods  of  board  fence? 

4.  In  a  farm  of  140  acres  there  are  7  acres  of  orchard.     What 

part  of  the  farm  is  the  orchard?     How  much  land  l^e- 
side  the  orchard? 

5.  A  grocer  selling  rice  in  7   pound  packages,  sold  3  pack- 

ages to  one  man  and  4  to  another.      How  many  pounds 
did  he  sell  to  both? 


6.  A  florist  sells  roses  which  cost  him  57  cents  per  dozen, 

for  95  cents  per  dozen.     How  much  does  he  gain  on 
7  dozen? 

7.  8S253  were    divided    equally   among   7   children.      How 

many  dollars  did  each  child  receive? 

8.  Mr.  Wood  had  $2891   and  spent  one-seventh  of  it.     How 

many  dollars  had  he  left?     What  part  of  his  money 
had  he  left  ? 

9.  A  lot  cost  $3747,  a  house  $2735,  a  barn  $878  and  a  side- 

walk f^l77.      Wliat  was  the  cost  of  all? 

10.  An    army   of  9287   men    engaged   in   battle.       1375   were 

killed  and  57  were  made  prisoners.     How  many  were 
left  in  the  army? 

11.  I  bought  170  cameras  for  $7   each.      I  sold  the  wdiole 

number  for  $1100.      Did  I  gain  or  lose,  and  how  much? 

12.  Mr.   Adams  owned  19  horses;    lie  kept  12  and  sold  the 

remainder  for  $S9().      How  much  did   he   receive   for 
each  horse  sold? 


124 


THE  RATIONAL  ARITHMETIC. 


A 

r-v 

r 

L 

1 

1 

n 

U 

r- 

r 

1 

J 

p 

U 

/-N 

U 

!• 

r\ 

n 

LJ 

1  1 

1  1 

1 

L 

1.  A  is  8.     How  many  8's  in  B?     How  many  in  C?     In  D? 

E?     F?     G?     H?     I?     J?     K?     L? 

2.  A  equals  8,  B  equals  10.     To  what  is  C  equal?     D?     E? 

F?     G?     H?     I?     J?     K?    L? 

3.  A  equals  what  part  of  B  ?     What  part  of  C  ?     Of  D  ?     E  ? 

E?     G?     H?     I?     J?     K?     L? 
4   8  is  what  part  of  16?     What  part  of  24?     Of  32?     40? 
48?     56?     64?     72?     80?     88?     96? 

5.  B  equals  how  many  A's?     What  part  of  C?     Of  D?     E? 

F?     G?     H?     I?     J?     K?     L? 

6.  16  is  how  many  8's?     What  part  of  24?     Of  32?     40? 

48?     56?     64?     72?     80?     88?     96? 

7.  C  equals  how  many  A's?     How  many  B's?     What  part  of 

D?     OfE?     F?     G?     H?     I?     J?     K?     L? 


PART   SECOND. 


125 


L  24  is  how  many  8's  ?     How  many  16's  ?     What  part  of  32  ? 
Of  40?     48?     56?     64?     72?     80?     88?     96? 

2.  D  equals  how  many  A's?     How  many  B's?     Hoav  many 

C's?      What  part  of  E?      Of  F?     G?      H?     I?     J? 
K?     L? 

3.  32  is  how  many  8's     How  many  16's?     How  many  24's? 

What  part  of  40 ?      Of  48?      56?      64?      72?      80? 
88?     96? 

4.  E  equals  how  many  A's?     How  many  B's?     How  many 

C's?     How  many  D's?     What  part  of  F?     Of  G?     H? 
I?     J?     K?     L? 

5.  40  is  how  many  8's?     How  many  16's?     How  many  24's? 

How  many  32's?      What  part  of  48?      Of  56?      72? 
80?     88?     96? 

"  "      B's?      C's?      D's?      E's? 

T7     r>  T      f» 


su :     oo  r     yo  r 
6.  F  equals    how   many   A's?      B's?      C's?      D 
What  part  of  G?     Of  H?     I?     J?     K?     L 

1  O'      O        TT 1  ^1„  O         TT „ 


equals    now    many   ii  s  r      .d  s  :       v_/  s  r       u  ni       ^  » i 
What  part  of  G?     Of  H?     I?     J?     K?     L? 
is  how  many  8's?    How  many  16's?    How  many  24's? 
How  many  32's?     Etc. 


2 

12 

22 

32 

8 

42 

52 

62 

72 

3 

13 

23 

33 

S 

43 

53 

63 

73 

4 

14 

24 

34 

8 

44 

54 

64 

74 

5 

15 

25 

35 

8 

45 

55 

65 

75 

6 

16 

26 

7 

17 

27 

8 

18 

28 

9 

19 

29 

36 

8 

46 

37 

8 

47 

38 

8 

48 

39 

8 

49 

56 

66 

76 

57 

67 

77 

58 

68 

78 

59 

69 

79 

Add  the  red  figure  to  each  number  in  the  same  large  square. 
Subtract  it  from  each  number  larger  than  itself.  Multiply 
and  divide  in  the  same  way. 


l-2() 


THE   RATIONAL   ARITIL\FETJC. 


1.   Add  upward,  downward,  by  lines  to  the  right  and  to  fclie 
left: 


8 

8 

8 

8 

8 

8 

8 

8 

8 

7 

8 

0 

5 

8 

1 

7 

8 

0 

7 

4 

8 

6 

2 

7 

8 

5 

8 

2 

8 

5 

3 

G 

8 

4 

3 

7 

G 

7 

4 

G 

8 

3 

4 

0 

.      8 

3 

4 

8 

2 

8 

8 

7 

8 

6 

4 

7 

1 

0 

8 

0 

8 

7 

3 

2.   Add,  subtract  and  multiply: 

32       24        IG       48        5G        72       G4       88       80       40 

8888888888 


13 

8 


25 

8 


37 

8 


49 

8 


79 

8 


88 
8 


G^ 


8 


98 
8 


38G 

8 


497 

8 


Divide 


8)1G  8)32  8)48  8)24  8)5G  8)12 


8)40  8)G4 


8)88 


X)9(i 


8)80  7)84 


4.  IG  equals  how  many  8'sy 
32  equals  how  many  8's? 
40  equals  how  many  8's? 
5G  equals  how  many  8's? 
88  equals  how  many  8's? 
80  equals  how  many  8's? 

5.  8  is   f^  of  ._ 


48  equals  how^  many  8's? 
G4  equals  how  many  8's? 
24  equals  how  many  8's? 
72  equals  how  many  8's? 
9G  equals  how  many  8's? 

49  equals  how  many  7's? 

8  is   I-  of 


PART   SECOND. 


1-2? 


0"? 


1.  8  is  1  of 


8  is 

1 

4 

of 

8  is 

1 

"9 

of 

8  is 

1 
1  0 

of 

8  is 

1 
1  1 

of 

♦  )  is 

1 

7 

of 

'J  is 

1 
1  1 

of 

8  is 

1 

of 

8  is 

G 

1 
8' 

> 

o 

8  is 

1 

7 

1 

of 

8  is 

of 

7  is 

1  2 
1 

of 

4  is 

1 

9 

of 

3  is 

1 

8 

of     _ 

In  34? 

In  27? 

In  (;3y 

In  SI? 

In  42? 

• 

In  (>7? 

In  30? 

In  98  ? 

2.  How  many  8's  are  there  in  17? 
How  many  8's  are  there  in  47? 
How  many  8's  are  there  in  50? 
How  many  8"s  are  there  in  71  ? 
How  many  8's  are  there  in  20? 
How  many  8's  are  there  in  59? 
How  many  8's  are  there  in  76? 
How  many  8's  are  there  in  85? 

3.  A  boy  picked  38  quarts  of  berries  in  one  week,  42  in  the 

second,  28   in  the  third,  and   18   in  the  fourth.     How 
many  quarts  did  he  pick? 

4.  In  one  school  there  are  858  scholars;  in  another  there  are 

684.     How  many  more  are   there  in  one  than  in  the 

other  ? 
A  man  traveled  284  miles  by  rail  and  8  times  as  far  by 

boat;  how  far  did  he  travel  by  boat? 
During  the  summer  a  family  used    248  quarts  of  milk. 

During  the  winter  they  used  g  as  much.      How  many 

quarts  did  they  use  during  the  winter? 

7.  If   one  boat   holds    5    persons;  how   many  boats  will   be 

needed  for  a  party  of  40  people? 

8.  In  an  orchard  there  are  56  trees  in  each  row,  and  \  as 

many  rows  as  there  are  trees  in  each  one;  how  many 
rows  are  there?     How  many  trees  in  all? 

9.  If  32  bushels  of  wheat  make  8  barrels  of  flour ;  how  many 

bushels  will  be  needed  to  make  64  barrels? 


o 


(J. 


128 


THE   RATIONAL   ARITHMETIC. 


1.  In  the  first  layer  of  blocks  in  this  solid,  how  many  rows  of 

4  blocks  each?  How  many  blocks  in  the  layer?  How 
did  you  find  this?  In  all  3  layers,  or  the  entire  solid, 
how  many  blocks  are  there?  How  did  yon  find  this? 
How  then  do  yon  find  the  number  of  cubic  feet  in  any 
solid  ? 

2.  How  many  inch  cubes  are  there  in  a  block  2  inches  long, 

2  inches  wide  and  1  inch  high?  See  ])age  68.  How 
many  inch  cubes  are  there  in  a  block  4  inches  long,  2 
inches  wide  and  1  inch  high? 

3.  HoAV  many  inch  cubes  are  there  in  a  block  6  inches  long, 

4  inches  wide  and  1  inch  high?  How  many  inch  cubes 
are  there  in  one  row?  How  many  of  these  rows  are 
there  in  the  block? 

4.  How  many  cubic  inches  are  there  in  a  box  that  is  4  inches 

long,  3  inches  wide  and  1  inch  high  ?     2  inches  high  ? 

3  inches  high? 

5.  How  many  cubic  inches  are  there  in  a  box  4  inches  long, 

2  inches  wide  and  2  inches  high? 

6.  A  block  containing  12  cubic  inches  is  3  inches  long  and  2 

inches  wide;  how  high  is  it? 


PART    SECOND.  129 

1.  A  pencil  box  containing  2-1:  cubic  inches  is  8  inches  wide 

and  1  inch  high;  how  long  is  it? 

2.  A  block  is  3  feet  long,  3  feet  wide  and  3  feet  high ;  how 

many  cubic  feet  does  it  contain?  What  is  the  area  of 
one  side  of  such  a  block  in  square  feet?  In  square 
yards?  How  many  cubic  yards  in  a  block  1  yard  long, 
1  yard  wide  and  1  yard  high?  How  many  cubic  feet 
in  such  a  block? 

3.  A  room  is   5  yards  wide,  7  yards  long  and  4  yards  high. 

How  many  cubic  yards  are  there  in  the  room  ? 

4.  A  cellar  is  7  yards  long,  6  yards  wide  and  3  yards  deep. 

How  many  cubic  yards  of  earth  were  taken  out  in 
diijficimj:  the  cellar? 

5.  The  foundation  of  a  house  is  equal  to  a  straight  wall  65 

feet  long,  4  feet  high   and   1|   feet  wide.     How  many 
cubic  feet  does  it  contain? 
0.   A  box  is   7   feet  long,  3  feet  wide  and  contains  03  cubic 
feet.      How  long  is  it? 

7.  A  bin  is  3  feet  wide,  4  feet  high   and  contains  72  cubic 

feet.     How  long  is  it? 

8.  A  coal-bin  is   12  feet  long,  0  feet  wide  and  7  feet  high. 

How  many  cubic  feet  of  coal  will  it  hold? 

9.  A  car  is  7  yards  lon<j,  4  yards  wide  and  3^-  yards  liisfh. 

How  many  cubic  yards  does  it  contain? 

10.  A  man  has  4  bins,  each  5  feet  long,  4  feet  wide  and  3  feet 

high.  How  many  cubic  feet  of  coal  will  they  hold  to- 
gether ? 

11.  A  bin  is  12  feet  long,  9  feet  wide  and  6  feet  high.     How 

many  cubic  yards  does  it  contain? 

12.  1  box  is  4  feet  long,  3  feet  wide  and  2  feet  high.     A  sec- 

ond is  5  feet  long,  3  feet  wide  and  2  feet  high.  A  third 
is  G  feet  long,  5  feet  wide  and  4  feet  high.  How  many 
cubic  feet  in  the  3  boxes? 


130  THE   RATIONAL  ARITHMETIC. 

1.  Review  page  74. 

2.  In  a  5-gallon  can,  liow  many  quarts  are  there?    How  many 

pints?     How  many  gills? 

3.  A  milk-rpan  started  in  the  morning  with   100  quarts  of 

milk.      How   many   pints   did   he   have?      How   many 
gallons? 

4.  There  are  8  people  in  a  family  and  each  one  drinks  -J  a 

pint  of  milk.      How  many  pints  must  be  bought?    How 
many  quarts? 

5.  From  a  jar  containing  2  gallons  of  mineral  water,  6  pints 

were  taken.     How  many  pints  were  left?     How  many 
quarts  ? 

6.  How  many  bottles  holding   2  quarts   each  can  be  filled 

from  20  gallons? 

7.  A  lamp  burns  a  quart  of  oil  every  24  hours.     How  many 

pints   must  be  bought  to  last   82   days?     How   many 
gallons  ? 


8.  A  milk-man  had  I7(>  <]uarts  of  milk.      How  many  gallons 

did  he  have? 

9.  How  many  gill  cups  can  be  filled  from  2  quarts  and  1  pint 

of  vinegar?     From  5  gallons? 

10.  Tliere  are  314^  ii^allons  in  a  barrel.    How  nuury  iJ^allons  are 

there  in  4  barrels?     In   G  barrels?     In   8   barrels?     3 
barrels?     5  barrels? 

11.  A  barrel  holds  31^  gallons?     How^  many  quarts  in  it? 

12.  From  a  barrel  of  gasoline  how  many  cans  may  be  filled  if 

each  holds  3  quarts?  How  many  if  each  holds  ^  a 
U-allon  ?  Ih  trallon  ? 
Id.  A  milk-man  starts  in  the  morning  Avith  48  gallons  of  milk. 
How  many  customers  can  he  serve  if  each  takes  3 
quarts?  How  many,  if  each  takes  2  quarts?  If  each 
takes  3  pints? 


PART   SECOND.  L'U 

1.  Review  page  76. 

2.  At  9^  a  peck,  what  Avill  2  bushels  of  oats  cost? 

8.   What  is  1  quart  o£  beans  worth  if  a  peck  is  worth  72^? 

4.  At  $2  a  peck,  how  many  bushels  of  clover  seed  can  be 

bought  for  §?88? 

5.  A  fruit  dealer  sold  3  pecks  of  nuts  at  8^  a  quart.     What 

did  he  receive  for  them  ? 
f).   A  farmer  picked  2  bushels  of  apples  from  one  tree  and  3 
bushels  from  another.      How  many  pecks  did  he  pick 
from  both  together? 

7.  A  grain  bin  holds  2  bushels.     How  many  pecks  do  7  such 

bins  hold? 

8.  During  the   summer  a   boy  picked  64  quarts  of  berries. 

How  many  pecks  did  he  pick?     How  many  bushels? 


9.   From  a  bushel  of  beans  2  quarts  and  1  pint  are  taken. 
How  many  quarts  are  left? 

10.  How  many  pint  boxes  of  cherries  may  be  filled  from  a 

peck  ? 

11.  A  man  paid  60(^  for  14  bushels  of  apples.      He  sold  them 

at  15^  a  peck.  How  much  did  he  receive?  How  much 
did  he  gain? 

12.  2  boys  gathered  6  bushels  of  nuts.     They  sold  5^  bushels 

by  the  peck.  How  many  pecks  did  they  sell?  The 
remainder  they  sold  by  the  quart.  How  many  quarts 
did  they  sell? 

13.  A  wheat  bin  holds  144  bushels.      If  340  pecks  are  taken 

out,  how  many  pecks  remain?     How  many  bushels? 

14.  A  farmer's  apple  orchard  yields   an   average  of  5  bushels 

per  tree.  If  there  are  75  trees  in  the  orchard,  Avliat  is 
the  entire  yield?  If  he  packs  them  in  barrels,  allowing 
3  bushels  to  a  barrel,  how  many  barrels  would  he 
require  ? 


132  THE   RATIONAL   ARITHMETIC. 

1.  How  long  will  it  take  to  travel  592  miles  on  a  bicycle  at 

the  rate  of  8  miles  an  hour? 

2.  A  squirrel  carried  into  his  hole  8  acorns  every  day.     How 

many  did  he  carry  in  8  Aveeks? 

3.  Find  the  cost  of  2  bushels,  3  pints  of  cherries  at  4^  a  pint. 

4.  AVhat  is  the  weight  of  8  tubs  of  butter,  each  weighing 

56^  pounds? 

5.  What  is  the  cost  of  12  pecks,  3  quarts  of  peas  at  8^  a 

quart  ? 

6.  What  is  the  cost  of  8  sacks  of  barley,  each  weighing  112 

pounds,  at  8^  a  pound? 

7.  How  many  pints  in  53G  gallons?     In  987  gallons? 

8.  How  many  quarts  in  498  pecks?     In  789  pecks?     In  586 

pecks?     In  379  pecks? 

9.  How  many  months  will  it  take  a  man  to  save  $1,000  if  he 

saves  $8  a  month? 

10.  How  many  pecks  in  2708  quarts?     In  7912  quarts?     In 

6856  qiiarts? 

11.  How  many  gallons  in  4584  pints?     In  9728  pints?     In 

8136  pints? 

12.  How  long  will  a  barrel  of  oil  containing  504  pints  last,  if 

8  pints  are  burned  each  week? 

13.  Find  the  weight  of  8  barrels  of  oat  meal,  each  containing 

192  pounds. 

14.  A  fruit-dealer  bought  8  barrels  of  apples  at  $2  a  barrel, 

each  barrel  containing  3  bushels.  He  sold  them  at  $1 
a  bushel.  How  much  did  he  get  for  them?  How 
much  did  he  gain? 

15.  Allowing  30  days  to  a  month,  how  many  days  are  there 

in  8  months? 

16.  A  farmer  had  420  bushels  of  wheat.      He  sold  J  of  it  to 

one  man  and  304  pecks  to  another.  How  many  bushels 
had  he  left  ? 


PART    SECOND.  133 

1.  There  are  9  horses  in  each  of  8  fields;  how  many  horses 

are  there  in  all? 

2.  If  a  person  works  8  hours  a  day,  how  many  hours  will  he 

work  from  Monday  morning  until  Saturday  night? 

3.  A  boy  was  asked  how  many  marbles  he  had,  and  replied 

that  if  he  had  8  times  as  many  he  would  have  56.      How 
many  had  he? 

4.  A  ship  sails  8  miles  an  hour.     At  the  same  rate,  in  how 

many  hours  will  it  sail  88  miles? 

5.  At  ^12  a  month,  how  much  is  the  rent  of  a  house  for  8 

months  ? 

6.  A  clerk  receiving  $12  a  week,  spends  $4  for  board.     If  he 

saves  the  rest,  how  much  will  he  have  in  8  weeks? 

7.  A  man  being  asked  the  value  of  his  horse,  said  he  would 

take  $96   dollars  for  him  although  he  was  worth  one- 
eighth  more.      What  was  the  horse  worth? 

8.  Mabel  is  20  years  old,  and  her  sister's  age  is  three-fourths 

of  hers.     How  old  is  her  sister? 

9.  At  8^  a  quart,  what  will  6  quarts  of  cranberries  cost? 

10.  A  horse  goes  9  miles  in  2  hours;  a  train  runs  8  times  as 

fast.     How  many  miles  will  the  train  run  in  the  same 
time  ? 

11.  How  much  is  hay  per  ton  when  $88  is  paid  for  8  tons? 

12.  A  horse  is  fed  a  peck  of  oats  a  day.     How  many  weeks 

will  42  pecks  last  him? 

13.  If  a  family  uses  2  quarts  of  milk  a  day,  at  4^/  a  quart  how 

much  will  the  bill  amount  to  in  8  days? 

14.  How  many  days  are  there  in  32  weeks? 

15.  If  1   jumping-rope  is   6  feet  long,  how  long  are  8  such 

ropes  together?     How  many  yards  long? 

16.  If  1  pint  of  oil  costs  3^,  what  will  4  quarts  cost? 

IT.   A  family  uses  6  pints  of  mineral  water  a  day.    How  many 
gallons  will  they  use  in  32  daj^s? 


134 


THE   RATIONAL   ARITHMETIC. 


W 


R 

t5 

e 


E 


^ 


G 


K 


n 

u 

1  1 

1  1 

1 

L^ 

1.   A  is  9.     How  many  9's  in  B?     How  many  in  C?     In  D? 


J?     K?     L? 

To  what  is  C  equal  ?    D  ?    E  ? 

K?     L? 

What  part  of  C  ? 

K?     L? 


E?     F?     G?     H?     I? 

2.   A  equals  9.      B  equals  IS. 
F?     G?     H?     I?     J? 

8.   A  equals  what  part  of  B  ? 
F?     G?     H?     I?     J? 

4.  9  is  what  part  of  18  ?     What  part  of  27  ? 

54?     63?     72?     81?     90?     99?     108? 

5.  B  equals  how  many  A's?     What  part  of  C? 

F?     G?     H?     i?     J?     K?     L? 
().   18   is  how  many   9's?     What  part  of  27? 
54?     63?     72?     81?     90?     99?     108? 

7.  C  equals  how  many  A's?     How  many  B's? 

D?     OfE?     F?     G?     H?     I?     J?     K?     L? 

8.  27  is  how  many  9's?     How  many   18's?     What  part  of 

36?     Of  45?     54?     63?     72?     81?     90?     99?     108? 


Of  D? 
Of  3()? 

Of  D? 
Of  36? 


E? 
45? 

E? 
45? 


What  part  of 


PART   SECOND. 


135 


1.  D  equals  how  many  A's?     How  many   B"s?     How  many 

C's?      What  part  of   E?      Of  F?     G?     H?     1?     J? 
K?     L? 

2.  36  is  how  many9's?     How  many  18's?     How  many  2T's? 

What  part  of  45 ?     Of  54?     63?     72?     81?     UO?     99? 
108? 

3.  E  equals  how  many  A's?     How  many  B's?     How  many 

C's ?     How  many  D's  ?     Wliat  part  of  F  ?     Of  G ?     H  ? 
I?     J?     K?     L? 

4.  45  is  how  many  9's?     How  many  18's?     How  many  27's? 

How  many  36's?    What  part  of  54?     Of  63?    72?    81? 
90  ?    99  ?     108  ? 

5.  F  equals  how  many  A's?     How  many  B's?     How  many 

C's?     How  many   D's?     How  many  E's?     What   part 
of  G?     Of  H?     I?     J?     K?     L? 

6.  54  is  how  many  9's?     How  many  18's?     How  many  27's? 

How  many  36's?     Etc. 


2 

12 

22 

32 

9 

42 

52 

62 

72 

6 

16 

26 

36 

9 

46 

56 

66 

76 

3 

13 

23 

33 

9 

43 

53 

63 

73 

7 

17 

27 

37 

9 

47 

57 

67 

77 

4 

14 

24 

34 

9 

44 

54 

64 

74 

8 

18 

28 

38 

9 

48 

58 

68 

78 

5 

15 

25 

35 

9 

45 

55 

65 

75 

9 

19 

29 

39 

9 

49 

59 

69 

79 

Add  the  red  figure  to  each  number  in  the  same  large  square. 
Subtract  it  from  each  number  larger  than  itself.  Multiply 
and  divide  in  the  same  way. 


136 


THE   RATIONAL   ARITHMETIC. 


1.  Add  upward,  downward,  by  lines  to  the  right  and  to  the 


left: 


9 

9 

9 

9 

9 

9 

9 

9 

9 

8 

9 

7 

6 

9 

4 

3 

2 

3 

7 

8 

9 

6 

5 

9 

9 

8 

4 

6 

9 

7 

9 

9 

4 

3 

9 

6 

5 

8 

9 

6 

9 

9 

9 

2 

5 

4 

9 

7 

9 

5 

9 

3 

9 

8 

3 

8 

9 

6 

9 

4 

9 

2 

7 

2 

9 

7 

9 

5 

9 

3 

9 

9 

1 

8 

9 

() 

9 

4 

9 

2 

8 

2.  Add,  subtract  and  multiply 


47 

68 

45 

89 

93 

77 

90 

64 

99 

9 

9 

9 

9 

9 

9 

9 

9 

9 

39        88        92  46        80  209  398       768  908 

9        _^       _^  Jl,        _^  _^  __?.      _^  _5 

3.  Divide: 

9)27           9)45  9)63  9)36           9)54  9)18 

9)72         9)108  9)90  9)81           9)99  8)96 


4.  27  equals  how  many  9's? 
54  equals  how  many  9's? 
63  equals  how  many  9's? 
18  equals  how  many  9's? 
72  equals  how  many  9's? 
99  equals  how  many  9's? 


45  equals  how  many  9's? 
36  equals  how  many  9's? 
81  equals  how  many  9's? 
90  equals  how  many  9's? 
108  equals  how  many  9's? 
72  equals  how  many  8's? 


PART   SECOND. 


137 


1. 

9 

is 

1 

T 

of 

9 

is 

1 
2 

of 

9 

is 

1 

of 

9 

is 

1 
'9 

of 

9 

is 

1 
1  0 

of 

9 

is 

1 
1  1 

of 

2.  How  many  9's  in  19?  In  29? 
How  many  9's  in  48  ?  In  56  ? 
How  many  9's  in  39?  In  65? 
How  many  9's  in  76?  In  109? 
How  many  9's  in  84?  In  98? 

3.  At  siglit,  name  the  sums: 

5  6  7  8  9  4 

4         7  8  9  3  9 


9  is  J  of 
9  is  J-  of 
9  is  i  of 
9  is  4  of 
9  is  ^ig-  of 
8  is  i  of 


8 
6 


7 
7 


7 
9 


5 
9 


5  6 

3  7 

2  3 


9 
5 


8 
6 
4 


7 
8 
6 


6 

9 
5 


5  7 
4          6 

6  9 


9 

8 


3 

9 

7 


10        41        22        53        84        75        30        67       98       59 
6  6  6  ()  6  6  (>  (>         6         6 


4.   At  sight,  name  the  differences: 


12 

15 

18 

17 

19 

16 

29 

25 

28 

29 

4 

6 

4 

6 

5 

4 

9 

3 

7 

10 

24 

26 

28 

26 

27 

25 

23 

28 

27 

29 

13 

12 

15 

14 

16 

14 

11 

15 

13 

16 

21 

22 

23 

24 

25 

27 

28 

26 

25 

24 

9 

6 

7 

8 

6 

9 

8 

9 

7 

1 ' 

6 

138  THE   RATIONAL   ARITHMETIC. 

1.  What  is  the  cost  of  4  dozen  eggs  at  9^  a  dozen? 

2.  What  is  the  cost  of  6  feet  of  mokling,  if  9  feet  cost  81^? 

3.  How  long  Avill  it  take   1   man  to  do  the  work  that  9  men 

can  do  in  11  days? 

4.  William   earns  one-ninth   as  much   money   as   his   father 


whose  wages  are  $08  a  month ;  how  much  does  William 
earn  a  month  ? 

5.  In  the  front  of  a  building  there  are  72  windows.      In  each 

story  there  are   9   windows;  how  many  stories  high  is 
the  building? 

6.  Jane's  grandfather  is   72  years  of  age,  and  Jane  is  one- 

ninth  as  old ;  in  how  many  years  will  she  be  17  ? 

7.  How  much  more  than  $36  should  a  man  have  in  order  to 

buy  9  tons  of  coal  at  $5  a  ton? 

8.  There  are  8  rows  of  seats  in  a  school-room,  and  9  seats  in 

each  row;  how  many  seats  in  the  room? 


9.   Find  the  cost  of  17  barrels  of  rice  at  $9  a  barrel. 

10.  I  Ixad  9  dozen  buttons   and  used  88  buttons.     How  many 

were  left?     How  much  did  I  pay  for  all  of  them  at  ()^ 
a  dozen  ? 

11.  A  steamer  sails  298  miles  a  day.     How  far  will  it  sail  in 

9  days  ?  * 

12.  I  bought  12  barrels  of  flour  at  $9  a  barrel,  and  sold  the 

flour  for  $95.      How  much  did  I  lose  ? 

13.  At  $158  an  acre,  what  will  9  acres  of  land  cost? 

14.  Alice  has  $11  and  her  father  has  9  times  as  much  and  $S 

more.      How  many  dollars  have  both? 

15.  A  certain  line  of  telegraph  costs  $985  a  mile.     How  much 

would  9  miles  cost? 

16.  What  is  a  man's  income  in  9  years  at  $2385  a  year? 

17.  A  gentleman  earns   $9   a  day  for  8  days,  and  spends  $8  a 

day  for  8  days.      How  much  has  he  left? 


PART    SECOND.  139 

1.  How  many  square  feet  in  a  square  yard? 

2.  A  blackboard  is  4  feet  wide  and  9  feet  long.     How  many 

square  feet  in  it?     How  many  square  yards? 

3.  Each  window  in  a  scliool-room  contains  9  square  feet.     In 

6  sucli  windows  there  are  how  many  square  feet?    How 
many  square  yards? 

4.  There  are  9  sheh^es  in  a  book-case;  each  one  contains  12 

books.      How  many  books  in  the  case? 

5.  One  end  of  a  desk  is  9  feet  from  the  wall,  the  other  end  is 

7  feet  from  the  opposite  wall.  The  desk  is  3  feet  and  6 
inches  long.  How  far  is  it  from  one  side  of  the  room 
to  the  other? 

6.  A  horse  travels   6  miles  an  hour.      How  far  will  it  go  at 

the  same  rate,  in  9  hours? 

7.  John  has  83^.     How  many  9^  books  can  he  buy,  and  how 

much  money  will  he  have  left? 

8.  A  boy  pays  12^  for  3  pencils.     At  the  same  rate  what  will 

9  pencils  cost? 


9.  In  each  of  9  cars  there  are  57  persons.     How  many  per- 
sons in  the  9  cars? 

10.  There  are  322  rails  to  the  mile  of  railroad  track.      Plow 

many  rails  in  9  miles  of  track? 

11.  There  are  9  equal  lots  fronting  on  a  street  378  feet  long. 

How  wide  is  each  lot? 

12.  A  man  owns  5  lots.     The  first  is  worth  $1,929,  the  second 

$959,  the  third  $1,195,  the  fourth  $1,699,  and  the  fifth 
$989.     What  is  the  value  of  the  5  lots? 

13.  A  boy  takes  9  subscriptions  to  the  Youth's  Companion  at 

$1.75    each.       How    much    money  did    he   receive  for 
them  all? 
11.   A   manufacturer  sold    9  carriages  at  $195   each.       How 
much  did  he  get  for  them? 


140 


THE    RATIONAL   ARITHMETIC. 


1  ounce      2  ounces 


4  ounces 


8  ounces 


16  ounces 
1  pound 


1.  Review  page  78. 

2.  How  many  ounces  are  there  in  1  pound?     In  2  pounds? 

3  pounds?     4  pounds?     (3  pounds? 

3.  What  part  of  1  pound  is  8  ounces  ?    4  ounces  ?    2  ounces  ? 

12  ounces? 

4.  Which   weight    shown  on   this  page  equals    J-   a   pound? 

Which  one  equals  -j^  of  a  pound  ?    Which  ^  ?    Which  ^  ? 

5.  Which  2  weights  together  equal  f  of  a  pound?     AVhicli  2 

together  |  of  a  pound? 
0.   The  8  ounce  weight  equals  Avhat  part  of   2  pounds?     Of  3 
pounds? 

7.  The  4  ounce  weight  equals  Avhat  part  of  2  pounds?     Of 

3  pounds? 

8.  The  8  ounce  and  the  4  ounce  weight  together  equal  what 

part  of  2  pounds?     Of  3  pounds? 

9.  100  pounds  are  called  a  hundredweight. 

10.  How  many  hundredweights  are  there  in  200  pounds?     In 

400  pounds? 

11.  How  many   pounds   are   there  in    i  of  a  hundredweight? 

i-  of  a  hundredweight?     |-? 

12.  If  a  grocer  has  different  weights,  as  shown  in  the  picture, 

which  ones  will  he  use  in  weighing  |-  of  a  pound  of  tea  ? 

Which  in  weighing  |-  of  a  pound  ?    -^\  of  a  pound  ?    y\  ? 

19        5   9       19       19        19       119       59      i  5  9       7. 9      X  3  9 
"3"  •        T"6  •        ¥  •        T  •        T^  •        T  6  •         8  *         16'         8  *         16- 

13.  Which  different  weights  may  he  use  in  weighing  1  J-  pounds 

of    rice?     In  weighing    1]   pounds?      IJ-  pounds?     11 
pounds  ?     If  ? 


PART   SECOND.  141 

1.  There  are  60  pounds  of  wheat  in  1  bushel.      How  many 

pounds  in  9  bushels V     In  7  bushels?     In  5  bushels? 

2.  1  hundredweight  of  metal  costs  $6.      What  will  50  pounds 

cost?     75  pounds?     25  pounds? 

3.  What  is  the  postage  at  |^  an  ounce  on  a  package  weigh- 

ing 4  ounces?     On  1|-  pounds?     On  3  pounds? 

4.  A  bushel  of  oats  weighs  32  pounds,  how  many  pounds  in 

a  peck?     In  a  quart?     In  3  pecks? 

5.  A  grocer  weighs  out  1|  pounds  of  butter.     What  weights 

does  he  use?     How  many  4  ounce  weights  will  he  use 
to  weigh  li  pounds?     I  pound?     2  pounds? 

6.  Find  the  value  of  4  pounds  and  8  ounces  of  pepper  at  20^ 

a  pound. 

7.  A  grocer  sells  8  packages  of  tea,  each  weighing  6  ounces ; 

how  many  ounces  do  all  weigh  together?     How  many 
pounds  ? 

8.  A  man  bought  GO  bags  of  flour,  each  weighing  5  pounds. 

HoAV  many  hundredweights  did  he  buy? 

9.  If  a  man  buys  old  iron  at  14^^'  a  pound,  what  will  lie  pay 

for  24  pounds?     For  |  a  hundredweight? 

10.  How  many  ounces  are  there  in  12  pounds? 

11.  A  farmer  sold  G   tubs  of  butter  averaging  in  weight  I  a 

hundredweight  each.        How  many  pounds  did  he  sell  ? 
How  many  ounces? 

12.  What  is  the  weight  in  pounds  of  3  packages,  one  weighing 

2^  pounds,  one  ^  a  pound    and   the  other  3  pounds? 
What  is  the  weight  in  ounces? 

13.  A  man  bought  3  packages  of  beans  weighing   8  pounds 

each ;  he  made  them  into  8-ounce  packages.    How  many 
packages    did  he  have? 

14.  A  grocer  sold  |^  of  a  pound  of  tea,  ^  a  pound  of  butter,  f 

of  a  pound  of  coffee,  and  1^  pounds  of  sugar.      How 
many  ounces  in  the  entire  sale? 


142 


1. 


THE   RATIONAL   ARITHMETIC. 


1 

X 

10 

— 

10 

X 

1 

2 

X 

10 

10 

X 

2 

— 

3 

X 

10 

10 

X 

3 

4 

X 

10 

10 

X 

4 

— 

5 

X 

10 

— 

10 

X 

5 

6 

X 

10 

10 

X 

6 

i 

X 

10 

10 

X 

7 

8 

X 

10 

— 

10 

X 

8 

9 

X 

10 

10 

X 

9 

— 

A 

/\ 

■ 

n 

U 

r> 

■1 

^ 

2.  How  many  lO's  in  A  ?     In  B  ?     In  C  ? 

3.  A  equals  what  part  of  B  ?     Of  C  ? 

4.  B  equals  how  many  A's?     What  part  of  C? 

5.  C  equals  how  many  A's?     How  many  B's? 

6.  10  is  what  part  of  20?     Of  30?     40?     50?     60?     70? 

SO?     90?     100?     110?     120? 

7.  20  is  how  many  lO's?     What  part  of  30?     Of  40? 

GO?     70?     80?     90?     100?     110?     120? 

8.  30  is  how  many  20's?     AVhat  part  of  40?     Of  50? 

70?     80?     90?     100?     110?     120? 

9.  40  is  how  many  20's?     How  many  30's?     What  part  of 

50?     Of  60?     70?     80?     90?     100?     110?     120? 
10.   50  is  how  many  20's?    How  many  30's?    How  many  40's? 
What  part  of  60 ?    Of  70?    80?    90?    100?    110?  120? 


50? 


60? 


PART   SECOND.  143 

1.  60  is  how  many  20's?     How  many  30's?     40's?     50'sV 

What  part  of  70?     Of  80?     90?     100?     110?     120? 

2.  70  is  how  many   20's?     How  many  30's?     4:0's?     50's?* 

60's  ?     What  part  of  80  ?     Of  90  ?     100  ?     110  ?     120  ? 

3.  80  is  how  many  20's?     How  many   30's?     40's?     50's? 

60's?     70's?    What  part  of  90?     Of  100?     110     120? 

4.  90  is  how  many   20's?     How  maiiy  30's?     40's?     50's? 

60's?     70's?     80's?     What  part  of  100?     110?     120? 

5.  100  is  how  many  20's?     How  many   30's?     40's?     50's? 

60's?     70's?     80's?     90's?     What  part  of    110?      Of 
120? 

6.  110  is  how  many  20's?     How  many  30's?     40's?     50's? 

60's?     70's?    80's?    90's?    lOO's?    What  part  of  120? 

7.  120  is  how  man   20's?     How  many  30's?     40's?     50's? 

60's?     70's?     80's?     90's?     lOO's?     llO's? 

8.  Add,  subtract  and  multiply: 

12      15      23      30      36      42      47      53      59      61      68 
10      10      10      10      10      10      10      10      10      10       10 


74      79 

80 

83 

88 

91 

98 

87 

59 

67       99 

10      10 

10 

10 

10 

10 

10 

10 

10 

10       10 

8. 

Divide : 

10)30 

10)50 

10> 

46 

10)60 

10 

)75 

10)29 

10)80 

10)67 

10)90 

10)38     10)100 

10) 

99 

10)110 

10)120 

10.   30  equals  how  many  lO's?  50  equals  how  many  lO's? 

40  equals  how  many  lO's?  70  equals  how  many  lO's? 

60  equals  how  many  lO's?  20  equals  how  many  lO's? 

90  equals  how  many  lO's?  110  equals  how  many  lO's? 

80  equals  how  many  lO's?  100  equals  how  many  lO'sr 

120  equals  how  many  lO's?  81  equals  how  many  9's? 


144 


THE   RATIONAL   ARITHMETIC. 


10  is 

1 

3 

of 

10  is 

1 
75 

of 

10  is 

1 

7 

of 

10  is 

1 
6 

of 

10  is 

1 
11 

of 

10  is 

1 
T2 

of 

7  is 

1 

7 

3 

or 

6  is 

1 

1  0 

of 

4  is 

1 

of 

R  i« 

1 

of 

1  2 


10  is  i- 

of 

10  is  i 

of 

10  is  i 

or 

10  is  1 

of 

10  is  ^v 

of 

9isl 

of 

8  is  i 

of 

5  IS  i\ 

of 

7  is  i 

of 

9is,V 

or 

In  50  ? 

In  47  ? 

In  70? 

In  100? 

In  125  ? 

2.  How  many  lO's  are  there  in  34? 
How  many  lO's  are  there  in  29? 
How  many  lO's  are  there  in  0(3? 
How  many  lO's  are  there  in  85? 
How  many  lO's  are  there  in  99? 

3.  What  is  the  sum  of  three  lO's  and  five  lO's? 
What  is  the  sum  of  four  lO's  and  five  lO's? 
What  is  the  sum  of  six  lO's  and  five  lO's? 
What  is  the  sum  of  five  lO's  and  five  lO's? 
What  is  the  sum  of  six  lO's  and  six  lO's? 

4.  Wliat  is  the  sum  of  40  and  five  lO's? 
What  is  the  sum  of  70  and  three  lO's? 
What  is  the  sum  of  85  and  two  lO's? 
What  is  the  sum  of  33  and  six  lO's? 
What  is  the  sum  of  110  and  nine  lO's? 
What  is  the  sum  of  130  and  four  lO's? 

5.  What  is  the  difference  between  121  and  six  lO's? 
What  is  the  difference  between  111  and  seven  lO's? 
What  is  the  difference  between  98  and  three  lO's  ? 
What  is  the  difference  between  143  and  nine  lO's? 
What  is  the  diff'erence  between  110  and  eiofht  lO's? 
What  is  the  difference  between  85  and  six  lO's? 
What  is  the  difference  between  93  and  four  lO's? 


PART    SECOND.  145 

1.  If  a  mail  works  10  hours  a  day,  how  many  hours  does  he 

work  in  one  week  not  inchiding  Sunday? 

2.  How  many  inches  in  10  feet? 

3.  How  many  eggs  in  10  dozen? 

4.  How  many  months  in  10  years? 

5.  How  many  square  feet  in  1  square  yard?     In  10  square 

yards  ? 

6.  If  there  are  10  square  feet  of  window  glass  in  one  win- 

dow, how  many  in  8  windows? 

7.  Mr.  Reed  had  70  sheep.     Wolves  killed  three- tenths  of 

them.     How  many  were  left? 

8.  How  many  square  inches  in  a  10  inch  square? 

9.  How  many  blocks  of  wood  1  foot  square  will  be  required 

to  pave  a  hall  that  is  10  feet  wide  and  11  feet  long? 

10.  How  many  square  feet  in   the  walls  of  a  room  that  is  10 

feet  high  and  10  feet  square? 

11.  It  is  6  miles  to  a  village.    A  man  goes  and  returns  5  days 

each  week.     How^  far  does  he  travel  in  1  week?     In  3 
weeks?     6  weeks?     10  weeks? 

12.  There  are  10  rooms  in  a  house.     In  each  room  there  are  2 

pictures  and  3  wdndow-s.      How  many  pictures  and  win- 
dows in  the  house? 

13.  In  one  car  each  seat  will  hold  5  persons,  in  another  6  per- 

sons and  in  another  3.     In  each  car  there  are  10  seats. 
How  many  persons  may  be  seated  in  the  3  cars? 
11.  A  train  of  4  cars  has  in  the  first  car  45  persons,  in  the 
second   54,  in   the   third   65,  in   the   fourth    59.      How 
many  persons  are  in  the  train? 

15.  A  ten  story  building  has  10  windows  in  each  of  the  first 

6  stories,  and  8  wdndows  in   each  of  the  remaining  4 
stories.     How^  many  windows  in  the  entire  buildiug? 

16.  A  table  is  10  feet  long,  4^  feet  wide.      What  is  its  peri- 

meter?    Its  area? 


146  THIO    NATIONAL   ARITHMETIC. 

1.  Review  page  80. 

2.  One  dollar  is  written  $1  or  $1.00. 

One  dollar  and  fifty  cents  is  written  $1.50. 

3.  Tlie  point  after  tlie  $1  shows  that  the  two  figures  on  the 

right  stand  for  cents,  and  the  figure  or  figures  on  the 
left  stand  for  dollars. 

4.  Two  dollars  and  twenty-five  cents  is  written  $2.25. 
Tliree  dollars  and  six  cents  is  written  $3.06. 

Ten  dollars  and  sixty  cents  is  written  110.60. 

5.  Head: 
;5.01     $9.10     $7.09     $10.20     $36.50     $30.03      $20.19 

S.02     14.15     $9.13     143.75     $84.62     $13.40     $12.05 

6.  If  any  number  of  cents,  as,  for  example,  25,  stands  alone 

with  no  dollars,  it  may  be  written  25(^,  or  $.25. 

7.  Read,  $.40,  $.16,  $.35,  $.50,  $.07,  $.10,  $.09. 

8.  Write  in  figures: 

Nine  dollars  and  twenty -five  cents;  forty  dollars. 
Twenty-six  dollars  and  six  cents;  fourteen  cents. 
Ninety  dollars  and  ninety  cents;  seven  cents. 
Tliirt)^  dollars  and  five  cents;  one  hundred  dollars. 

9.  What  is  the  sum  of  1   quarter,   2  dimes  and   1   nickel? 

Write  the  answer. 

10.  What  is  the  sum  of    3  half-dollars,   1   quarter,   2  dimes 

and  5  pennies?     AVrite  the  answer. 

11.  If  you  pay  for  a  3-cent  car  fare  with  a  quarter,  in  what 

coins  may  your  change  be  given  you? 

12.  A  street-car  conductor  collects  72  five-c(^nt  fares  in  one  trip. 

How  much  money  does  he  collect? 

13.  A    girl    buys   flowers    worth   40^/.      If   she   has   quarters, 

dimes,  nickels  and  pennies,  with  what  different  coins 
may  she  pay  for  them  ? 

Note. — Have  dollars,  half  dollars,  quarters,  dimes,  nickels  and  pen- 
nies where  they  may  be  observed  and  handled.  Toy  money  will  serve 
the  purpose. 


PART    SECOND.  14^ 


1.  Add: 
$1.55 

.08 
4.50 
5.17 

8.69 

$9.76 
3.72 
1.31 

7.75 
.87 

$9.30 
12.10 
17.68 
24.33 

9.77 

$25.71 

20.04 

47.37 

.75 

8.10 

$85.94 

57.38 

19.99 

6.43 

.98 

2.  Subtract: 

$56.29 
15.25 

$54.54 
24.32 

$13.74 
7.53 

$99.99 
93.94 

$107.60 
89.10 

$10.34 

7.25 

$45,32 
22.50 

$77.55 
35.95 

$321.76 
.  145.09 

$446.82 
128.72 

3.  Multiply: 

$2.63 
2 

$16.24 
3 

$37.58 
4 

$56.17 
5 

$10.29 
5 

$207.20 
7 

$450.75 
6 

$327.06 

7 

$525.50 
8 

$290.40 
9 

4.  Divide: 

2)$56.24      2)$38.56      3)$27.96      3)$45.21      4)1416.72 

4)$892.64    5)$125.75    5) $530. 50    6)$426.84    6)$558.72 
7)$637.84  8)$968.72  8)  $656. 32  9)  $468. 63 

5.  I  bought  a  horse  for  $97.00,  kept  him  at  a  livery  stable 

for  six  months  at  $12.00  a  month,  and  then  sold  him 
for  $175.00.     Did  I  gain  or  lose,  and  how  much? 

6.  Mr.  A.  had  $756.48.     Mr.  B.  had  $327.16  and  Mr.  C.  had 

$258.92.     How  much  did  they  all  have  together? 


148 


THE   RATIONAL   ARITHMETIC. 


1  X  11 

2  X  11 

3  X  11 

4  X  11 

5  X  11 

6  X  11 

7  X  11 

8  X  11 

9  X  11 
10  X  11 


11  X  1  =  - 

11  X  2  =:  _ 

11  X  3  =  . 
11  X  4  =^  _ 
11  X  5  =^  _ 
11  X  6  =  - 
11  X  7  ==  _ 
11  X  8  =  _ 
11  X  0  =^  _ 
11  X  10  = 


—  - 

A 

/\ 

n 

U 

2    How  many  ll's  in  A?     In  B? 

3.  A  equals  what  part  of  B  ? 

4.  B  equals  liow  many  A's?. 

n.   11  is  what  part  of  22?     Of  33?    44?    55?    66?    77     88? 

99?     110?     121?     132? 
(;.   22  is  how  many  ll's?      What  part  of  33?      Of  44?      55? 

06?     77?     88?     99?     110?     121?     132? 

7.  33  is  how^  many  ll's?     How  many  22's?     What  part  of 

44?     Of  55?     66?     77?     88?     99    110?    121?    132? 

8.  44  is  how  many  ll's?       How  many  22's?       How  many 

33's?      What  part  of  55?      Of  m?      11?      88?     99? 
110?     121?     132? 


TART    SECOND.  149 

1.  55  is  how  many  ll's?     How  many  22's?     33's?     44's? 

What  part  of  66?      Of  77?      88?     99?     110?     121? 
132? 

2.  66  is  how  many   ll's?     How  many  22's?     33's?     44's? 

55's?     What  part  of  77?     Of  88?     99?     110?     121? 
132? 

3.  77  is  how  many  ll^s?     How  many  22's?     3B's?     44's? 

55's?     66's?     What  part  of  88?'  Of  99?     110?    121? 

132? 
4   88  is  how  many  ll's?     How  many  22's?     33's?     44's? 

55's?    66's?'77's?    AVhat  part  of  99?     Of  110?    121? 
5.  99  is  how  many  ll's?     How  many   22's?     33's?     44's? 

55's?    ^66's?'   77's?     88's?      What  part  of  110?     Of 

121?     132? 
0.   IIU  is  how  many  ll's?     How  many  22's?     33's?     44's? 

55's?     66's?     77's?     88's?     99's?    What  part  of  121? 

Of  132? 

7.  121  is  how  many  ll's?     How  many  22's?     33's?     44's? 

55's?     66's?     77's?     88's?    99's?    llO's?     What  part 
of  132? 

8.  132  is  how  many  ll's?     How  many  22's?     33's?     44's? 

55's?     66's?     77's?     88's?     99's?     llO's?     121's? 

9.  Add,  subtract  and  multiply: 

39   45   50   23   47   56   73   65   89   29   99 

n     nnnnniiiiiiiiii 

93   70   84   38   87   49   96   27   71   59   77 
11   11   11   11   11   11   11   11   11   11   11 


10.  Divide: 

11)33      11)55      11)77      11)^      11)44     11)66     11)59 

11)77  11)69  11)110  11)88  11)121  11)99  11)132 


150 


THE   RATIONAL   ARITHMETIC. 


1.  33  equals  how  many  ll's? 
66  equals  how  many  ll's? 
44  equals  how  many  ll's? 
99  equals  how  many  ll's? 
110  equals  how  many  ll's? 
88  equals  how  many  ll's? 


55  equals  how  many  ll's? 

22  equals  how  many  ll's? 

77  equals  how  many  ll's? 
121  equals  how  many  ll's 
132  equals  how  many  ll's? 

84  equals  how  many    7's? 


2.  11 

11 

11 

11 

11 

11 

(] 

7 

5 

7 


s  J  of 
s  I  of 
s  I  of 
s  4-  ol 

S  yV  of 
S    yV   ^^ 

s    I    of 

s  tV  of 
s^of 


s  -iV  of 


3.  How  many  ll's  are  there  in  35? 
How  many  ll's  are  there  in  28? 
How  many  ll's  are  there  in  61? 
How  many  ll's  are  there  in  89? 
How  many  ll's  are  there  in  111? 

4.  How  many  ll's  are  there  in  88? 
How  many  ll's  are  there  in  66? 
How  many  ll's  are  there  in  99? 
How  many  ll's  are  there  in  55? 
How  many  ll's  are  there  in  39? 

5.  What  is  the  difference  between  five  ll's  and  three  ll's? 
What  is  the  difference  between  seven  ll's  and  four  ll's? 
What  is  the  difference  between  eight  ll's  and  five  ll's? 
What  is  the  difference  between  nine  ll's  and  seven  ll's? 
What  is  the  difference  between  six  ll's  and  two  ll's? 


11  is  J 

of 

11  is   l- 

of 

11  is  i 

of 

His  i 

of 

11  is  ,V 

of 

8  is  1 

or 

9  is  -t 

of 

6  is  3^2 

of 

8  is  i 

of 

9is  i 

of 

In  57  ? 

In  45  ? 

In  79  ? 

In  100? 

In  125? 

In  74? 

In  85? 

In  76  ? 

In  65  ? 

In  43  ? 

PART    SECOND.  151 

1.  What  is  the  perimeter  of  an  11  inch  square? 

2.  What  is  the  area  of  an  11  inch  square? 

3.  3  loads  of  hay  will  winter  one  cow.      How  many  cows  will 

33  loads  winter? 
■4.  How   many  inches  in   3  feet?     In   5  feet?     7  feet?     11 
feet? 

5.  How  many  square  inches  in  a  rectangle  that  is  11  inches 

long  and  3  inches  wide?  11  inches  long  and  5  inches 
wide?  11  inches  long  and  7  inches  wide?  11  inches 
long  and  9  inches  wide?  11  inches  wide  and  12  inches 
long? 

6.  How  many  days  in  11  weeks  and  4  days? 

7.  Find  the  cost   of   one-eleventh   of    55   sheep  at  5  dollars 

each  ? 

8.  What  is  the  cost  of  three-elevenths  of  121  cords  of  wood 

at  ^5  a  cord? 

9.  Find  the  cost  of  one-eleventh  of  22  sheep  at  $7  each.     Of 

three-elevenths  at  $9  each. 

10.  I  paid  §110  house  rent  and  one-eleventh  as  much  for  gas. 

How  much  did  I  pay  for  both? 

11.  Isaac  planted  132  seeds  in  11  hills.     How  many  seeds  did 

he  put  in  one  hill? 

12.  How  many  square  inches  in  the  top  of  a  mantel  that  is 

11  inches  wide  and  48  inches  long? 

13.  All  but  one-eleventh  of  §99  was  divided  among  3  people. 

How  much  did  each  receive? 

14.  How  many  feet  of  ribbon  Avill  be  required  to  bind  a  port- 

folio that  is  11  inches  square,  allowing  4  inches  extra 
for  corners?     How  many  yards? 

15.  What  is  the  perimeter  of  a  rectangle   7  by  11  inches? 

What  is  its  area? 

16.  It  is  11  miles  from  A  to  B.     How  far  will  one  travel  in 

making  4  round  trips? 


152 


THE   RATIONAL   ARITHMETIC. 


1.    1  X  12  = 

2  X  12  = 

3  X  12  = 

4  X  12  . 

5  X  12  = 

6  X  12  = 

7  X  12  = 

8  X  12  = 

9  X  12  = 

10  X  12  - 

11  X  12  = 


12  X  1  = 

12  X  2  = 

12    X    3    :: 

12    X    4    r 

12  X  5  3 
12  X  6  = 

12    X    7    :: 

12    X    8    r 

12  X  9  -- 
12  X  10 
12  X  11 


A 

/\ 

2.  How  many  12's  in  A? 

3.  12  is  what  part  of  24?      Of  86?     48?     (U)?     72?     84? 

96?     108?     120?     132?     144? 

4.  24  is  how  many  12's?     What  part  of  36?     Of  48?     60? 

72?     84?     96?     108?     120?     132?     144? 

5.  36  is  how  many  12's?     How  many  24's?     What  part  of 

48?    Of  60?    72?    84?    96?    108?    120?    132?    144? 

6.  48   is   how   many   12's?      How  many   24's?     How  many 

36's?     What  part  of  60?      Of  72?     84?     96?     108? 
120?     132?     144? 


PART   SECOND.  153 

1.  GO  is  how  many  12's?         How  many  24"s?     36's?     48's? 

AVliatpartof72?    OfS4?    96?    108?    120?    132?    144? 

2.  72  is  liow  many  12's?     How  many  24's?     36's?     48's? 

60's?     What  part  of  84?     Of  96?     108?     120?     132? 
144? 

3.  84  is  how  many  i2's?     How  many  24's?     36's?     48's? 

60's?      72's?       What  part  of  96?       Of  108?      120? 
132?     144? 

4.  96  is  how  many  12's?     How  many  24's?     36's?     48's? 

60's?      72's?      84's?      What  part  of  108?      Of  120? 
132?     144? 

5.  108  is  how  many  12's?     How  many  24's?     36's?     48's? 

60's?     72's?     84's?     96's?      What  part  of  120?     Of 
132?     144? 

6.  120  is  how  many  12's?     How  many  24's?     36's?     48's? 

60's?      72's?      84's?      96's?      108's?      What  part  of 
132?     Of  144? 

7.  132  is  how  many  12's?     How  many  24's?     36's?     48's? 

60's?     72's?      84's?      96's?      108's?      120's?     What 
part  of  144? 

8.  144  is  how  many  12's?     How  many  24's?     36's?     48's? 

60's?     72's?      84's?      96^s?      108's?     120's?     132's? 

9.  Add,  subtract,  and  multiply: 

28      53      45      33      48      57      74      66      90      38    •  99 
12121212      12      121212121212 

67      89      78      49      96      50      87      29      82      59      88 
12      12      12      12      12      12      12      12      12      12      12 


10.  Divide: 

12)36   12)60  12)72   12)_28  12)49   12)_56   12)66 

12)71  12)108  12)99  12)120  12)84  12)144  12)132 


154 


THE   RATIONAL  ARITHMETIC. 


1.  86  equals  how  many  12's? 

48  equals  how  many  12's? 

24  equals  how  many  12*s? 
108  equals  how  many  12's? 

96  equals  how  many  12's? 
144  equals  how  many  12's? 


60  equals  how  many  12's? 

72  equals  how  many  12's? 

84  equals  how  many  12's? 

132  equals  how  many  12's? 

120  equals  how  many  12's? 

121  equals  how  many  ll's? 


12  is 

1 

or 

12  is 

1 

(5 

or 

12  is 

1 

8 

of 

12  is 

1 

1 

of 

12  is 

1 
1  1 

of 

12  is 

1 
1  2 

of 

10  is 

1 
9^ 

of 

His 

1 
8 

of 

7  is 

1 
10 

of 

9  is 

1 

7 

of 

12 

is 

1 

"2 

of 

12 

is 

1 

'4 

of 

11 

is 

1 
6 

of 

12 

is 

1 
9 

of 

12 

is 

1 
1  0 

of 

9 

is 

1 
•8 

of 

11 

is 

1 
8" 

of 

9 

is 

1 

12 

of 

11 

is 

1 

IT 

of 

10 

is 

1 
1  0 

of 

In  4( 

)? 

In 

52? 

In 

74? 

In 

107? 

In  142? 

3.  How  many  12's  are  there  in  49? 
How  many  12's  are  there  in  29? 
How  many  12's  are  there  in  65? 
How  many  12's  are  there  in  87  ? 
How  many  12's  are  there  in  112? 

4.  What  is  the  sum  of  40  and  two  12's? 
What  is  the  sum  of  21  and  four  12's? 
What  is  the  sum  of  23  and  six  12's? 
What  is  the  sum  of  104  and  eight  12's? 
What  is  the  sum  of  36  and  fiA^e  12's? 
What  is  the  sum  of  16  and  seven  12's? 

5.  What  is  the  difference  between  72  and  two  12's? 
What  is  the  difference  between  96  and  seven  12's? 
What  is  the  difference  between  100  and  five  12's? 
What  is  the  difference  between  104  and  six  12's? 
What  is  the  difference  between  144  and  four  12's? 
What  is  the  difference  between  236  and  three  12's  ? 


PART   SECOND.  155 

1.  Keview  pages  82  and  83. 

2.  How  many  months  old  is  a  boy  who  is  7  years  old?     How 

many  Aveeks  old  is  one  who  is  11  months  old? 

3.  How  many  months  old  is  a  boy  who  is  11  years  old?     12 

years  old? 

4.  How  many  weeks  in  6  months? 

5.  How  many  minutes  in  one-half  a  day? 

6.  How  many  minutes  from  7.15  a.  m.  to  8  o'clock  a.  m.  ? 

7.  How  many  minutes  from  8  o'clock  p.  m.  to  9.15  p.  m.  ? 

8.  How  many  hours  from  5  in  the  morning  until  9  at  night? 

9.  A  boy  goes  to  bed  at  9  o'clock  and  gets  up  at  6.     How 

long  is  he  in  bed? 
10.   A  boy  plays  ball  in  the  morning  from  7  until  9,  and  in 

the  afternoon  from  1  until  6.     How  many  hours  does 

he  play? 
11    A  train  leaves  Chicago  at  9  o'clock  in  the  morning  and 

arrives  in  Cincinnati  at  6  in  the  evening.      How  many 

hours  is  it  on  the  way? 

12.  A  train    leaves    Chicago    at    10.30    in   the  morning    and 

reaches  Buffalo  at  12.20  at  night.  How  many  hours  is 
it  on  the  way? 

13.  A  train  leaves  Burlington  at  9  o'clock  in  the  morning, 

and  reaches  Chicago  at  2.15  in  the  afternoon.  How 
many  hours  is  it  on  the  way? 

14.  A  train  leaves  Peoria  at  11.40  a.  m.,  reaches  Streator  at 

1.33  p.  m.,  and  Chicago  at  4.30  p.  m.  How  long  is 
it  on  the  way  from  Peoria  to  Streator?  How  long  from 
Peoria  to  Chicago? 

15.  A  boat  leaves   Chicago  at  8.30  in  the  morning,  reaches 

Milwaukee  at  11.30,  and  leaving  Milwaukee  at  6.15  in 
the  evening,  reaches  Chicago  at  9.15.  How  many 
hours  does  it  take  to  make  the  round  trip?  How  many 
hours  from  the  time  the  boat  leaves  Chicago  until  it 
returns  ? 


J  56  THE   RATIONAL   ARITHMETIC. 

1  hour  1  day  1  week       1  year 

60  minutes        24  hours        7  days        365  days 

52  weeks 
12  months 

1.  How  many  minutes  in   1  hour?     In  2  hours?     3  hours? 

5  hours?  8  hours?  One  half  an  hour?  One-fourth 
of  an  hour?     Three-fourths  of  an  hour? 

2.  What  part  of  an  hour  are  10  minutes?     30  minutes?     45 

minutes?     15  minutes? 

3.  How  many  hours  in  a  week? 

4.  How  many  weeks  in  147  days? 

5.  A  boy  is  8  years  and  4  months  old.      How  many  months 

okl  is  he? 

6.  The  train  leaves  the  station  at  8.05.     It  is  a  12  minutes' 

walk  to  the  station.  At  what  time  must  one  start  in 
order  to  catch  the  train  ? 

7.  A  boy  leaves  home  at  7.30  each  morning  and  returns  from 

work  at  6.15  in  the  evening.  How  long  is  he  away 
from  home?     How  long  is  he  away  in  6  days? 

8.  A  train  leaves  the  station  at  7.15  and  arrives  in  the  city 

at  7.42  in  the  morning.  Returning,  it  leaves  the  city 
in  the  evening  at  5.40  and  arrives  at  6.11.  How  long 
does  a  man  spend  on  the  train  who  goes  back  and  forth 
each  day  for  10  days? 

9.  A  boy  leaves  home  for  school  at   8.35  and  reaches  the 

school  room  at  2  minutes  before  9.  He  returns  home 
for  lunch  at  noon,  taking  the  same  time  on  the  way  each 
trip.    How  long  is  he  on  the  way  in  1  day?    In  5  days? 

10.  School  begins  at  9  o'clock  and  dismisses  at  15  minutes 

before  12;  opens  at  1.30  and  closes  at  3.45.  How  long 
is  the  forenoon  session?  How  long  is  the  afternooB 
session?     How  long  are  both  together? 

11.  If  15  minutes  were  allowed  for  recess  both  morniug  auC 

afternoon,  how  long  would  the  sessions  be  together? 


PART   SECOND.  15 


■*/ 


1.  The  months  of  the  year  are: 

1.  January  (Jan.)  5.  May  9.  September  (Sept.) 

2.  February  (Feb.)  6.  June  10.  October  (Oct.) 

3.  March  (Mar.)  7.  July  11.  November  (Nov.) 

4.  April  (Apr.)  8.  August  (Aug.)  12.  December  (Dec.) 

2.  What  is  the  second  month  ?    Fifth  month  ?    Ninth  month  ? 

Sixth    month?       Eighth    month?       Eleventh     month? 
Twelfth  month  ? 

3.  Learn  the  order  of  the  months  by  number  and  name. 

4.  Seven  of  the  months  have  31  days  each,  four  have  30  days 

each  and  one  28  days.     How  many  days  in  the  year? 

5.  The  first,  third,  fifth,  seventh,  eighth,  tenth  and  twelfth 

months  have  31   days,  the  others  have  30  days,  except 
February  which  has  28  generally,  but  in  Leap  year  29. 

6.  How  many  days  in  all  of  the  months  containing  31  days? 

How  many  days  in  all  the  months  containing  30  days? 

7.  How  many  days  in   January?      April?      March?      Feb- 

ruary?    June?     August?     Septeml)er?     July?    Octo- 
ber?    November?     December? 

8.  How  many  days  in  the  first  3  months  of  the  year?     In 

the  last  3  months  of  the  year? 

9.  How  many  days  in  the  first  6  months  of  the  year  ?    In  the 

last  6  months  of  the  year? 

10.  How  many  days  difference  between  Ihe  first  6  months  and 

the  last  6  months  of  the  year? 

11.  How  many  days  in  February,  March  and  xlpril  together? 

12.  In  April,  May  and  June  together? 

13.  In  July  and  August  together? 

14.  In  September,  October  and  November  together? 

15.  A  man  left  home  in  the  morning  the  first  day  of  April  and 

returned  home   in   the   evening   the  last   day  of  July. 
How  many  days  was  he  away  from  home? 

16.  How    many   days   in   the   first,    third,    fifth,  seventh    and 

eighth  months  together? 


158  THE   RATIONAL   ARITHMETIC. 

1.  If  $24  pays  for  8  yards  of  silk,  how  many  yards  can  be 

bought  for  $12? 

2.  What  5  equal  numbers  make  75? 

3.  How  many   oranges   worth    4^   each    must   be    given    in 

exchange  for  16  lemons  worth  3^  each? 

4.  William  paid  half  a  dollar  for  a  reader,  a  quarter  of  a 

dollar  for  a  music  book  and  a  dime  for  a  tablet.     How 
much  did  he  pay  for  all? 

5.  If  4  lemons  cost  3^,  what  will  two  dozen  lemons  cost? 

6.  In  800  pints  how  many  quarts  are  there?     Hov/  many 

gallons  ? 

7.  It  requires  64  rods  of  fence  to  go  around  a  square  lot. 

How  long  is  one  side  of  the  lot? 

8.  What  is  the  rent  of  a  house  for  a  year  at  $12  per  month  ? 

9.  What  is  the  cost  of  3  bushels  of  corn  at  10^  a  peck? 

10.  A  boy  worked  8  days  for  50^  a  day  and  then  had  |6.     How 

much  had  he  before  beginning  the  work? 

11.  Edward  can  make  a  kite  in  8  days,  working  3  hours  a 

day.     How  many  days  will  it  take  him  if  he  works  6 
hours  a  day? 

12.  How  much  did  it  cost  Lewis  to  visit  the  World's  Fair  12 

days,  if  he  paid  each  day,  20^  for  car  fare,  50^  f(^r  his 
admission  ticket  and  40^  for  lunch  ? 

13.  How  many  feet  are  there  in  5044  inches? 

14.  Find  the  entire  cost  of  11  pounds  of  tea  at  60^  per  pound; 

25  pounds  of  sugar  at  7^;  124  pounds  of  soap  at  10^; 
and  18  barrels  of  flour  at  $8.37  per  barrel? 

15.  A  man  bought   a  horse   for   $85.50,   and  a  carriage  for 

$53.80  more  than  the  cost  of  the  horse.     What  was  the 
cost  of  both? 

16.  A  farmer  raised  8750  bushels  of  wheat.     He   sold  one 

half  of  it  to  one  man  and  4200  bushels  to  another  man. 
How  many  bushels  did  he  have  left? 


PART   SECOND.  150 

1.  Harold  has  86  specimens  in  liis  stamp  album.     His  father 

gave  him  12  more.      How  many  had  he  then  ? 

2.  A  street  car  conductor  collected  12  5 -cent  fares  and  12 

3-cent  fares  on  one  trip.     How  much  did  he  collect? 

3.  One  l3oy  can  jump  3^  feet  high;  another  boy  can  jump  12 

inches  Jiiglier.     How  high  can  the  second  boy  jump? 

4.  A  railroad  track  is  made  at  the  rate  of  12  miles  a  month. 

How  many  miles  of  track  can  be  made  at  the  same  rate 
in  one  year?     In  IJ  years y     In  2^  years? 

5.  '.>Tn  ball   cartridges  were  distributed  among  the  members 

of    a    com])any    of    soldiers.       Each    received    12    car- 
tridges  and  there   were   10  left.     How  many   soldiers 
were  there  in  the  company? 
0.   A  lady  spent  54  months   away  from  home.      How  many 
years  was  she  away  ? 

7.  How  many  minutes  from  (5  o'clock  in  the  morning  until  6 

at  night? 

8.  How  many  yeai's  are  9,87G  months  equal  to? 

9.  A  boy  left  home  at  tlie  age  of  13.     He  was  gone  until  he 

was  55.      How  many  months  was  he  away  from  home? 

10.  At  11  cents  a  dozen,  what  will  180  Inittons  cost? 

11.  A  tailor  uses  000  buttons  every  month,  and  puts  12  on  each 

garment.      How  many  garments  does  he  make? 

12.  Mr.  Brown's  salary  is  ^2,500  a  year.     How  much  is  it  a 

month  ? 

13.  Find  the  cost  of  12  gallons  and  2  quarts  of  syrup  at  11 

cents  a  quart. 

14.  On  each  side  of  the  street  there  are  09  trees.     What  did 

it  cost  to  plant  them,  at  12  dollars  each? 

15.  For  7  yoke  of  oxen  I  paid  $84  a  yoke  and  sold  them  all 

for  .^875.     Did  I  gain  or  lose,  and  how  much? 

16.  12  dozen  eggs  cost  $2.40.     What  will  5  dozen  cost? 

17.  How  many  square  inches  in  a  square  foot? 


160  THE   RATIONAL  ARITHMETIC. 

1.  If  4  tons  of  coal  cost  $24,  what  will  be  the  cost  of  2  tons  ? 

2.  How  many  bushels  are  |  of  54  bushels? 

3.  In  how  many  days  can  4  men  dig  a  ditch  that  2  men 

can  dig  in  12  days? 

4.  What  is  the  cost  of  2  pecks  of  beans  at  3^  a  quart? 

5.  George  now  has  $50.     How  much  will  he  have  if  he  saves 

$7  a  week  for  4  weeks  ? 

6.  If  a  man  buys  old  iron  at  ^^  a  pound,   how  much  will  he 

pay  for  48  pounds  ? 

7.  What  are  4  pecks  of  cherries  worth  at  10^  a  quart? 

8.  At   10^   a   pound,    how  many   pounds   of  grapes   can   be 

bought  for  90^'  and  30^'  together? 

9.  John  earned  |  as  much  as  Henry.     If  Henry  earned  32^, 

how  much  did  both  earn  ? 
10.   What  will  2  gallons  of  oil  cost  at  6(K/  a  quait? 


11.  How  many  feet  in  a  line  512  inches  long? 

12.  I  sold  a  watch  that  cost  $75  so  as  to  gain  |  of  the  cost. 

How  much  did  I  sell  it  for? 

13.  Find  the  difference  between   nine   thousand   eighty    and 

seven  thousand  seven  hundred  six. 

14.  How  many  tablets  at  9^-  each  can  be  bought  for  $82.08? 

15.  How  many  years  will  it  take  a  man  to  save  $2880,  if  he 

saves  $12  a  month? 

16.  A  building  is  240  feet  long  and  200  feet  wide.   How  many 

yards  is  it  around  the  building? 

17.  What  is  the  difference  in  value  between  12  lots  at  J^225 

each  and  a  house  at  $9500? 

18.  There  are  96  boxes  of  soap,  each  containing  60  pounds. 

How  many  ])ackages  of  4  pounds   each   (^an  be  made 
from  the  soap? 

19.  How  long  will  a  barrel  of  oil,  containing  51  gallons,  last, 

if  2  quarts  are  burned  each  day  ? 


PART   SECOND.  IBl 

L   What  will  be  the  cost  of  50  feet  of  rope  at  4^  a  foot? 

2.  I  pay  for  room  rent  $S  a  month,  and  for  office  rent  19  a 

month.      How  much  do  I  pay  a  year  for  both? 

3.  How  many   r)alls  weighing  8  pounds  each  will  equal  in 

weight  (i  balls  weighing  12  pounds  each? 

4.  How  many  pounds  of  grapes  at  4^  a  pound  must  be  given 

for  a  dozen  apples  worth  3^  each? 

5.  AVhat  will  be  the  cost  of  6  sheep,  if  12  sheep  cost  $60? 

0.   How  loni;  will  it  take  6  men  to  do  the  work  that  5  men 
can  do  in  12  days? 


7.  A  bushel  of  wheat  weighs  4  pounds  more  ihan  a  bushel 

of  corn.  What  is  the  difference  in  weight  between  845 
bushels  of  wheat  and  845  bushels  of  corn  ? 

8.  Four  loads  of  coal  weigh  respectively,  194H  pounds,  2104 

pounds,  1852  pounds  and  2468  pounds.  If  the  coal 
were  divided  equally  among  5  families,  how  many  pounds 
will  each  family  receive? 

9.  In  tiling  a  hall,  4878  tiles  were  l)ought,  but  two-ninths  of 

them  were  returned.  How  many  tiles  were  used  in 
tiling  the  hall  ? 

10.  How  many  strips  of  carpet  one  yard  wide  will  be  required 

to  cover  a  floor  that  is  27  feet  long  and  18  feet  wide? 
How  many  yards  of  carpet? 

1 1 .  How  many  square  inches  in  the  top  of  a  table  three  feet 

square  ? 

12.  AVliat  will  11  copies  of  Robinson  Crusoe  cost  at  38  cents 

per  copy? 

13.  How  many  pews  in  a  church  that  will  seat  760  persons,  if 

5  persons  can  be  seated  in  each  pew?  If  each  pew  will 
hold  only  4  persons? 

14.  I  can  buy  a  quart  of  cherries  for  12  cents.     At  that  rate, 

what  should  I  pay  for  7  bushels? 


162  THE   RATIONAL   ARITHMETIC. 


AVEITING   AND   READING   NUMBERS. 

1.  0,  I,  2,  3,  4,  5,  (),  7,  S.  1) 

2.  How  many  diffei-ent  ciiaracters  are  given  above? 

All  numbers,  no  matter  liow  large,  may  be  represented  by 
these  figures. 

3.  243 

Reading  tlie  3  alone  we  say  3  ones.  Reading  tlie  4  alone 
we  say  40  or  4  tens.  Reading  the  2  alone  we  say  200 
or  2  hundreds. 

4.  If  we  were  to  write  above  each  figure  a  separate  name  it 

would  appear:) 

i/i 

a        i/i        w 

n      p]      oj 
w     ^     § 

2    4   :^ 

But  if  we  were  to  call  these  all  ones,  we  would  read  it  as 
243  ones  or  units. 

5.  How  Avould  you  read  3,243? 

(1  This  new  figure,  3,  placed  before  the  other  nundjer,  we 
call  thousands.      How  then  would  you  read  10,243? 

7.  Large  numbers  are  divided  into  periods  of  3  places  each, 
thus  243  is  one  period.  3,243  has  2  periods.  These 
periods  are  separated  l)y  commas,  for  convenience,  as 
f  olloAvs : 

OlK'S 




a 

111 

C!j 

(H 

Ifl 

^3 

, 

P! 

fl 

W 

w 

O 
J5 

3 

<o 

H 

HH 

H 

6 

9,   4    5    6 
8.  How  mr.ny  periods  in  the  following  numbers?     Separate 
the  ])eriods  by  commas: 
346  4684  26  3781  1032 


PART   SECOND.  163 

1.  Read  the  following  numbers,  pointing  off  periods: 

5784  8752  0872  6875  7365 

3586  7678  6498  8988  8989 

2987  5425  5674  7988  6543 

2.  Write  the  following  numbers,  with  ones  in  the  right  hand 

column,   with   tens,  hundreds    and  thousands   in   their 

columns  as  shown  on  the  opposite  page: 
Seventeen.      Two  hundred  twenty-seven.      One   hundred 

seven. 
Thirty-one.     Three  hundred  twelve.      One  hundred. 
Sixty-eight.     Sixty  hundred  eighty.     Nine  hundred. 
One  thousand.     Eleven  thousand.     Eight  hundred. 
One  thousand  two  hundred.     Six  hundred  twentv-tive. 
One  thousand  sixty.     Two  hundred  seventy-five. 
One  thousand  six  hundi'ed  fifty.      One  hundred  seven. 
One  thousand  ten.      One  thousand  one  hundred. 
Five  thousand  six  hundred  fifty-five.      Nine  hundred. 
Three  thousand  three  hundred.      Seventy -five. 
Three  thousand  thirty.     Four  hundred  twenty -five. 
Six  thousand  six.     Eight  hundred  seventy-nine. 

3.  Write  in  Avords  or  read  from  the  page: 

125      683  1200 

307      469  3049 

590      303  5060 

483      791  2009 

4.  In  writing  numbers  for  addition   and   subtraction,    it   is 

more  convenient  to  place  ones  underneath   cnies,  tens 
under  tens,  hundreds  under  hundreds,  etc. 

5.  Write  for  addition  the  following  numbers: 

640,        35,        1282,        6,        821,        64,       8,       2305 

6.  Write  the  following  for  subtraction: 

From  872  take  6.     From  6475  take  242.     From  3684 
take  27. 


4816 

5090 

1010 

9847 

5064 

3005 

3100 

4200 

lU  THE   RATIONAL   ARITHMETIC. 

1.  Review  pages  90  and  91. 

2.  Add  2495 

0837 

12  7  and  5  are  12 

12  3  tens  and  9  tens  are  12  tens 

12  8  hundreds  and  4  hundreds  are  1200 

8  6  thousands  and  2  thousands  are  800() 


3.  A  simpler  way  in  whicli  to  set  down  the  answers  in  addi- 

tion is  to  pat  under  each  column  only  the  right  hand 
figure  of  the  sum  of  that  column,  and  to  place  the  left 
hand  figure  of  the  sum  above  the  next  column,  to  ])e 
added  with  it. 

4.  In  this  way  add  the  above  numbers: 

J  21  Adding  ones,    5 -)- 7  =  12,   or    1   ten   and   2; 

2495     place  the  2  in  the  right  hand  column  of  the  sum, 

6837     and  the  one  ten  above  the  9  in  tens'  column. 

9332  Adding  tens,  3  +  9  +  1  =  13  tens,  or  1  hun- 
dred and  3  tens;  place  the  3  tens  in  tens'  col- 
umn in  the  sum,  and  the  1  huiulred  above  tlie 
4  in  hundreds'  column. 

Adding  hundreds,  8  -f"  ^  +  1  =  13  hundreds, 
or  1  thousand  and  3  hundreds;  place  the  3  hun- 
dreds in  hundreds  column  in  the  sum,  and  the  1 

thousand  above  the  2  in  thousands  column. 
Adding  thousands,  0  -j-  2  -|-  1  =  9  thousands, 

which  place  in  thousands'  column  in  the  sum. 

5.  In  the  same  way  add: 

2037  8220  4587  1284  7431  33G8  3G43 
4250    975   3624   7536   1869   4852   5892 

4768  3579  1928  4536  5948  6384  7403 
1359   2468   3746   2879   3726   1597   1859 


PART   SECOND.  165 

1.  Add: 

121  Adding  ones,  5  -|-  9  +  4  =  18,  or  1  ten  and 

2564  8 ;  ]>lace  the  8  in  the  ones'  column  of  the  sum, 
1879  and  the  1  ten  above  tens'  column. 
4195  Adding  tens,  9  +  7  +  (J  +  1  =  23  tens,  or  2 
8638  hundreds  and  3  tens;  ])lace  the  3  tens  in  tens' 
column  in  tlie  sum,  and  the  two  hundreds  above 
hundreds'  column. 

Adding  hundreds,  l-\-H-\~^-\-2=W  hun- 
dreds, or  1  thousand  and  6  hundreds;  place  the 
6  hundreds  in  hundreds'  column  in  the  sum, 
and  the  1  thousand  above  thousands'  column. 

Adding  thousands,  4  +  1  4-  2  +  1  ~  8  thous- 
ands, which  place  in  thousands'  column  in  the 
sum. 


2.  In  the  same  way 

add : 

1729 

3546 

1892 

1563 

2623 

1089 

2703 

2354 

1273 

4203 

2427 

1206 

721 

3145 

4162 

2098 

461 

5314 

4257 

5147 

605 

1431 

1754 

2574 

256 

1714 

2425 

2804 

947 

6126 

1245 

4678 

6924 

3987 

3004 

2753 

825 

3256 

963 

728 

4058 

289 

1388 

1268 

1367 

2837 

1256 

874 

1452 

5234 

1834 

2756 

1234 

473 

1498 

3257 

3.  A  man  had  5  farms.     In  the  first  there  were  160  acres,  in 

the  second  88  acres,  in  the  third  275  acres,  in  the 
fourth  96  acres  and  in  the  fifth  324  acres.  How  many 
acres  in  the  fiA^e  farms? 

4.  There   are   375   pupils    in   one    school    building,    640  in 

another,  and  583  in  anotiier.  How  many  in  the  three 
buildings  ? 


166  THE   RATIONAL   ARITHMETIC. 

1.  A  man  paid  $2684  for  a  house,  $398  for  fiirnitiire  and 

$265  for  a  horse  and  carriage.  How  much  did  he  pay 
for  all  ? 

2.  A  lot  cost  $1540,  the  sidewalk  $116,  the  house  $6535,  the 

barn  $975.     How  much  did  they  all  cost? 

3.  A  ship  sailed  234  miles  the  first  day,  275  miles  the  second 

day,  and  the  third  day  as  far  as  in  the  first  two.  How 
far  did  it  sail  in  the  three  days? 

4.  Three  vessels  are  loaded  with  copper.     The  first  carries 

347  tons,  the  second  1256  tons,  the  third  4384  tons. 
How  many  tons  do  they  all  carry? 

5.  From  Chicago  to  Detroit  it  is  284  miles;  from  Detroit  to 

Buffalo,  251  miles;  from  BufPalo  to  New  York  City,  410 
miles.  How  far  is  it  from  Chicago  to  Buffalo?  How 
far  is  it  from  Chicago  to  New  York? 

6.  From  Chicago  to  St.  Louis  it  is  282  miles;  from  St,  Louis 

to  Kansas  City,  277  miles.  How  far  is  it  from  Chicago 
to  Kansas  City  by  the  way  of  St.  Louis? 

7.  From  Chicago  to  Burlington  it  is  206  miles;  from  Bur- 

lington to  Omaha,  296  miles;  from  Omaha  to  Lincoln, 
39  miles;  from  Lincoln  to  Denver,  484  miles.  How 
far  is  it  from  Chicago  to  Omaha?  From  Chicago  to 
Lincoln?     From  Chicago  to  Denver? 

8.  From  Chicago  to  Milwaukee  it  is  85  miles;  from  Mil- 

waukee to  La  Crosse,  281  miles;  from  La  Crosse  to  St. 
Paul,  131  miles;  from  St.  Paul  to  Minneapolis,  10 
miles.  How  far  is  it  from  Chicai^^o  to  La  Crosse? 
From  Chicago  to  St.  Paul?  From  Chicago  to  Minne- 
apolis?    From  Milwaukee  to  St.  Paul? 

9.  From  the  above  distances,  find  how  far  it  is  through   Chi- 

cago from  New  York  to  St.  Louis.  From  New  York  to 
Kansas  City.  To  Omaha.  To  Denver.  To  St.  Paul. 
To  Milwaukee. 


PART   SECOND.  167 

1.  A  man  IiRvS  156  books  in  one  case,  275  in  another  and  in  a 

third  145  more  than  in  both  of  the  others.  How  many 
books  has  he  in  the  B  cases? 

2.  A  factory  made  540  bicycles  in  January;  87 5  in  Febru- 

ary; 643  in  March,  and  856  in  April.  Hoav  many  did 
it  make  in  the  4  months? 

3.  A  man  delivered  4  loads  of  coal.     In  the  first  were  2150 

pounds;  in  the  second,  1975  pounds;  in  the  third,  2260 
pounds,  and  in  the  fourth,  2315  pounds.  How  many 
pounds  were  delivered  in  the  4  loads? 
1.  A  carpenter  was  paid  it^l375.50  for  building  one  house; 
$3240.75  for  another;  '^1658.50  for  a  third.  How 
much  did  he  receive  for  building  the  3  houses? 

5.  The  cash  sales  of  a  certain  merchant  were  on  Monday, 

$253.25;  Tuesday,  $167.54;  AVeduesday,-  $365.80; 
Thursday,  ^453.65;  Friday,  $385.42,  and  on  Saturday, 
$563.85.     Wliat  were  the  cash  sales  for  the  week? 

6.  A  man  bought  a  lot  for  $2154.    He  paid  $453  for  grading 

and  digging  a  cellar,  and  $165.40  for  a  sidewalk.  He 
built  a  house  to  cost  the  same  amount  that  he  had  spent 
for  the  lot  and  all  improvements.  How  much  did  he 
invest  in  the  lot  and  house? 

7.  A  man's  salary  was  $2300  a  year.    He  also  received  $135 

interest,  $426  rents,  and  from  all  other  sources  a  sum 
equal  to  these  three  amounts.  AVhat  was  his  annual 
income  ? 

8.  The  yield  from  one  field  of  wheat  was  275  bushels;  from 

a  second,  562i  bushels;  from  a  third,  458  bushels,  and 
from  a  fourth,  346|-  bushels.  What  was  the  entire 
yield  from  the  4  fields? 

9.  From  A  to  B  is  416  feet  and  6  inches;  from  B  to  C,  375 

feet;  from  C  to  D,  456  feet  and  6  inches.  How  far  is 
it  from  A  to  D  ? 


168  THE   RATIONAL   ARITHMETIC. 

1.  Eeview  page  93. 

2.  Subtract  247  from  5()  i.  ' 

7  ones  cannot  be  subtracter! 

564  =  550  +  14  from  4  ones.     Change  564  to 

247  =  240  +     7  550  +  14.        Subtracting,    7 

3jQ  _l_     rj  __  p^^^     from  14  irr  7;    240  from  550 

=:310.     310  +  7  =  317. 

3.  A  simpler  way  to  wiite   the  numbers  in  subtraction  is  to 

place  above  each  figure  that  figure  to  which  it  is  to  be 
changed. 

4.  In  this  way  subtract  the  above  numbers, 

5  j4         7  cannot  be  subtracted  from  4.     564  must  be 

564     changed  to  550  -+-  14.     The  5  in  hundreds'  place 

247     stays  unchanged;    the  6   tens  become  5  tens, — 

317     place  the  5  above  the  6  tens;  the  1  ten  left  from 

the  6  tens  is  added  to  the  4  to  make  14,— so  place 

the  14  above  the  4. 

Subtracting:  7  from  14  =  7;  4  tens  from  5  tens 
=  1  ten;  2  liundreds  from  5  jiundreds  =  3  hun- 
dreds. 

5.  Subtract  4526  from  6352. 

5,i3,4,r2         ^>  cannot  be  subtracted  from  2.      5  tens  and  2 
6352     must   be  changed  to  4  tens  +  12;  place  the  4 
452()     above  the  5  tens,  and  the  12  above  the  2. 
1826         Snl)tracting:  6  from   12  =  6;  2  tens  from   4 
tens  =  2  tens. 

But  5  hundreds  cannot  be  subtracted  from  3 
]iu)idreds.  6  thousands  and  3  hundreds  must 
be  clianged  to  5  thousands  +  13  hundreds;  place 
the  5  above  the  6  thousands  and  the  13  above 
the  3  jiundreds.  Again  subtracting:  5  hun- 
dreds from  13  hundreds  =  8  hundreds;  4  thous- 
ands from  5  thousands  =  1  thousand. 


PART  SECOND.  ini) 

1.  Subti'Hct: 

572  744  683  567  452    334    695 

246  527  256  439  326    128    478 

2.  Subtract: 

4283  3172  7395  6476  5746   8374   9547 

2657  1854  5868  3849  2828   5407   5618 


.S12 
2  16 


Subtract  4687  from  9374. 

T  cannot  ])ft  subtracted  from  4.      7  tens  and  4 
^,fi4     must   be  changed  to  6  tens  +  14;  place   tlie  () 
9  3  7  4     above  tlie  7  tens,  and  the  14  above  the  4. 
46  8  7  Subtracting:     7  from  14  =  7. 

4  ()  g  7  But  8  tens  cannot  be  subtracted  from  6  tens. 

3  hundreds   and  6  tens  must   be  changed  to  2 
liundreds  -\-  16  tens;  place  the  2  above  the  3  Jiundreds 
and  tlie  16  above  the  6  tens. 
Subtracting:     8  tens  from  If)  tens  =  8  tens. 
But  6   liundreds  cannot  be  subtracted  from   2  hundreds- 
9  thousands   and   2  hundreds   must   be   changed  to   8 
thousands  +  12    hundi'eds;    place    the   8   above   the   9 
thousands  and  the  12  above  tlie  2  hundreds. 
Subtractino-:      6    hundreds   from    12   hundreds  =  6   hun- 

CD 

dreds;  4  thousands  from  8  thousands  =  4  thousands. 
4.  Subtract: 

4352   6234   8132   9457   5321   3324   7563 
2676   1395   5786   3869   1867   1657   2786 


8967 

8241 

7241 

7294 

7182 

9256 

6842 

3429 

3819 

39s 

5076) 

3647 

7498 

3715 

7586 

6493 

4250 

8593 

5721 

5345 

3248 

4729 

7279 

3809 

2675 

3629 

170  THE   RATIONAL   ARITHMETIC. 

1.  A  farm  cost  $3215.     The  buildings  cost  $627  less  than 

the  farm.     How  much  did  the  buildings  cost? 

2.  One  railroad  has  5214  miles  of  track;  another  has  2767 

miles   of  track.      How  much  more  track  has  the  first 
than  the  second? 
o.   A  gentleman's  income  one  year  w^s  $1985  and  the  next 
year  it  was  $2140.      How  much  greater  was  his  income 
the  second  year? 

4.  Two  vessels  start  fi'om  tlie  same  point  at  the  same  time 

and  in  the  same  direction.  The.  one  travels  <S29  miles 
while  the  second  is  traveling  1014  miles.  How  far  are 
they  apart? 

5.  One  car  contains  35.852  pounds  of  coal,  another  contains 

20,475  pounds.     How  much  more  does  the  first  contain 
than  the  second? 
0.  A  merchant  sold  goods  which  cost  him  $2345,  for  $2610.50. 
What  was  his  p]*ofit? 

7.  A  man  gave  $9456  to  a  church  and  $5050  to  a  school,  how 

much  more  did  he  give  to  the  church  than  the  school? 

8.  From   Ohicago  to  Cairo,   Illinois,   it  is  365  miles;    from 

Chicago  to  Jackson,  Miss.,  it  is  732  miles,  and  from 
(yliicago  to  New  Orleans,  915  miles.  How  far  is  it 
from  Cairo  to  .lac^kson  ?  From  Cairo  to  New  Orleans  ? 
Fi'om  Jackson  to  New  Orleans? 

9.  From  Chicago  to  Indianapolis  it  is  194  miles;  from  Chi- 

cago to  Cincinnati,  ))09  miles,  and  from  Chicago  to 
AVashington,  903  miles.  How  far  is  it  from  Indianapo- 
lis to  Cincinnati?  How  far  from  Indianapolis  to  Wasli- 
iuo^ton?  HoAv  far  fr(nn  Cincinnati  to  Washin^Jfton? 
10.  From  Cliicago  to  Buffalo  is  539  miles;  from  Chicago  to 
Albany  is  837  miles;  fi'om  Chicago  to  Boston,  1038 
miles.  How  far  is  it  from  Buffalo  to  Albany  ?  From 
Buffalo  to  Boston?     From  Albany  to  Boston? 


PART   SECOND.  171 

1.  The  walls  and  ceilings  of  one  room   contain  444  square 

feet;  tliose  of  a  second  room  contain  liit>  sf|iiHre  feet 
less;  how  many  square  feet  in  the  second  room? 

2.  A  gentleman's  salary  is  $2(>5()  a,  year;  it'  liis  expenses  for 

the  same  time  are  §2025,  liow  much  does  he  save  in  one 
year  ? 
o.   The  land  of  a  farm   is  valued  at  $5785  and  the  huildiiigs 
on  it  at  §2450.      How   inucli   more   is   the   land   worth 
than  the  buildings? 

4.  One   farmer  raises  7519  bushels  of   corn;   another  i)H[H') 

bushels;  how  much  more  corn  does  the  first  man  raise 
than  the  second? 

5.  One   soldier  spent   8  years   and   5   months  in   the  army; 

another  spent  2  years  and  7  months;  how  many  months 
longer  was  the  first  soldier  in  the  army  than  the  second? 
0.  In  buying  horses  a  man  paid  §120  each  for  two  horses 
and  $105  each  for  three  others.  How^  much  less  did 
the  first  two  toi^ether  cost  than  the  last  three  toirether? 

7.  One  tank  of  water  holds  200  barrels;  a  second  taidv  holds 

185  barrels;  a  third  150;  how  much  more  does  the  first 
tank  hold  than  the  second?  Than  the  third?  How 
much  more  do  the  first  and  second  together  hold  than 
the  third?  The  second  and  third  together  than  the 
first? 

8.  If  on(5  ship  sails   045   miles  in   3   days,  and  another  sails 

717  miles  in  the  same  time,  how  mach  farther  does  the 
second  sail  than  the  first?  At  the  same  rate,  how  much 
farther  would  it  sail  in  one  day  ?     In  9  days  ? 

9.  The  expenses  of  one  boy  in  college  were  $755  a  year;  the 

expenses  of  another  boy  for  the  same  time  were  §105 
less;  of  a  third  boy  for  the  same  time  §150  less  than 
those  of  the  second.  What  were  the  expenses  of  the 
second  and  third  boys? 


173  THE   RATIONAL   ARITHMETIC. 

1.  Beview  page  95. 

2.  Multiply  4,  6,  8,  10,  3,  5,  7,  9,  11,  each  by  10.     In  each 

case,  wlnit  do  you  do  when  multiplying  by  10? 
n.  Multi[)ly  14,  25,  73,  243,  549,  each  l)y  10. 

4.  To  niulti|)]y  one  nund)er  by  finother  number  ending  with 

on(?  or  more  ciphers,  is   (M]uh1   to   multiplying  by  the 
left  hand  figures  and  adding  the  ci})hers  to  the  answer. 

5.  In  this  way  multiply  24  by  20. 

Place  the  20  so  that  the  2  comes  beneath  the  4  of 
24       24,  leaving  the  ci])her  to  the  right,  to  be  placed  at 
20     tlio  right  ot*  the  answer. 


480         Multiplying:     2  X  4  ==  8;  2x2  =  4;    add  the 
cipher,  and  we  have  480. 
(').   Multiply: 

84       90        75        68        237  485         379  946 

20        ;'>()        40        50          00  70           SO  90 

37        49        54        124        272  234        563  847 

200      300      400        500        600  700        800        900 


7.  Multiply  24  by  13. 

24  Since  13  is  10  +  3,  multiplying  24  by  13 

13  e(j[uals  the  sum  of  24  X  3  and  24  X  10. 

72     24  X  :^> 
240     24  X  10 

312 

8.  Multiply  76  by  15. 

76  76  X  15  =  7(]  X  5  and  7()  x  10. 

15 

380     76  X  5 
760     76  X  10 

1140 


PART   SECONIJ.  173 

1.  Multiply  53  by  24. 

53  53  X  24  =  53  X  4  and  53  x  20. 

24 

212  53  X  4 
1060  53  X  20 

1272 

2.  Multiply  134  by  45. 

134  134  X  45  =  134  X  5  and  134  x  40. 

45 


070 

134 

X  5 

5360 

134 

X  40 

6030 

3.  67 

35 

50 

76 

145 

476 

308 

714 

974 

23 

32 

43 

53 

37 

27 

83 

75 

523 

416 

312 

206 

102 

560 

345 

234 

630 

67 

22 

51 

34 

27 

46 

35 

18 

42 

297 

267 

285 

526 

808 

132 

114 

125 

863 

28 

35 

19 

25 

36 

47 

66 

48 

62 

169 

273 

286 

299 

473 

308 

315 

651 

943 

13 

44 

88 

120 

62 

73 

160 

23 

92 

4.  School  is  in  session  6  hours  a  day.      How  many  hours  is 

it  in  session  during  26  weeks  of  5  days  each? 

5.  There  are  95  rows  in  a  potato  field,-  if  it  takes  2  bushels 

to  plant  one  row  how  many  bushels  will  it  take  to  plant 
the  entire  field? 

6.  A  ship  can  sail  225  miles  a  day  in  fair  weather,  and  160 

miles  a  day  in  stormy  weather.     How  many  miles  can 
it  sail  in  7  days  if  3  of  these  days  are  stormy  ? 


174  THE   RATIONAL  ARITHMETIC. 

1.  A  merchant  buys  4  dozen  pairs  of  slioes  at  $2.25  per  pair. 

How  much  did  they  cost? 

2.  A  boy  reads  one  book  of  31 G  pages  every  2  weeks  during 

the  year.     How  many  pages  does  he  read  in  the  year? 

3.  There  are  189  teachers  in  the  schools  of  a  city.     Each  one 

lias  49    scholars    enrolled.       How    many  scholars    are 
there  in  the  city? 

4.  A  lot  is   195   feet  long  and   53   feet  wide.       How  many 

square  feet  does  it  contain? 

5.  A  train  runs  37  miles  in  an  hou)-.     How  far  will  it  run  in 

two  days  at  the  same  rate? 

6.  A  man  bought  37  horses  at  $09  each.      How  ranch  did 

they  cost  him  ? 

7.  A  merchant  bought  149  rolls  of  carpet.     Each  roll  con- 

tained 68  yards.    How  many  yards  of  carpet  did  he  buy  ? 

8.  There  are  8  cars  an  hour  on  a  street  car  line,  and  each 

carries  3G  persons.  How  many  persons  ride  on  the 

road   from  (>    o'clock  in    the   morning  until    G  in  the 
evening  ? 

9.  A  conductor  collects  27  5^'  fares,  and  G  3^^  fares  on  each 

trip  for  9  trips.      How  much  money  does  he  collect? 

10.  A  ]>oy  gets  $3.75  a  week  and  spends  2V)^'  each  week.      How 
•    much  money  will  he  have  at  the  end  of  IS  weeks  at  the 

same  rate? 

11.  A  boy  sells  29  papers  each  day  G  days  in  a  week.      How 

many  papers  does  he  sell  in  a  year? 

12.  If  there  are   17   apples  in  half  a  peck,  how  many  apples 

are  there  of  the  same  size  in  13  bushels? 
1)^  A  miller  bought  118  bushels  of  wheat  at  78^/  a  bushel. 

How  much  did  it  cost  him? 
14.  A  boy  makes  up  a   club   of   17   subscribers   for  Har])er's 

Young  reo])lo  at  $1.G5  each.      How  much  money  should 

he  collect? 


PART   SECOND.  175 

What  is  the  cost  of  the  foHowiiig  articles? 

1.  138  pounds  of  creamery  butter  at  18^/  a  pound? 

2.  215  pounds  of  dairy  butter  at  ITr/-  a  pound? 

3.  348  dozen  strictly  fresh  eggs  at  9^f  a  dozen  ? 

4.  48  bushels  of  new  potatoes  at  85^/  a  bushel? 

5.  464  pounds  of  turkeys  at  8?//  a  pound? 
(*).  '-*>7S  pounds  of  chickens  at  D^-  a  pound? 

7.  17  barrels  of  choice  apples  at  $3.25  a  bai-rel? 

8.  21)  barrels  of  common  apples  at  Jjj>2.35  a  barrel? 
*).  ()7  bunches  of  bananas  at  78^-  a  bunch? 

10.  29  boxes  of  lemons  at  |2.75  a  box? 

11.  19  boxes  of  California  oranges  at  $1.95  a  box? 

12.  13  crates  of  pineapples  at  $3.75  a  crate? 

13.  23  crates  of  tomatoes  at  $2.35  a  crate? 

14.  17  barrels  of  sweet  potatoes  at  $3.75  a  barrel? 

15.  378  pounds  of  white  sugar  at  44^/  a  pound? 
If).  456  pounds  of  yellow  sugar  at  4y-  a  pound? 

17.  17  bags  of  coffee  at  $5.83  per  bag? 

18.  14  tons  of  timothy  hay  at  $9.50  a  ton? 

19.  275  bushels  of  barley  at  43^-  a  Imsliel? 

20.  58  bushels  of  No.  1  wheat  at  $1.05  a  bushel? 
2i.  (;5  bushels  of  No.  2  wheat  at  98^/  a  ])usJiel? 

22.  165  bushels  of  No.  1  corn  at  42^/  a  busliel? 

23.  235  bushels  of  No.  2  corn  at  39^-  a  bushel  ? 

24.  256  bushels  of  white  oats  at  344^'  a  bushel. 

25.  27  bales  of  cotton  at  $6.34  a  bale? 

26.  47  barrels  of  flour  at  $(>  50  a  barrel  ? 

27.  39  bags  of  bran  at  $1.35  a  bag? 

28.  464  pounds  of  corn  meal  at  1^^  a  pound? 

29.  19  barrels  of  buckwheat  flour  at  $3.25  a  barrel? 

Note. — These  problems  may  be  varied  each  week,  or  (nich  month,  Ijy 
taking  the  market  quotations  in  the  newspapers  and  substituting  the  prices 
quoted  for  those  given  in  the  problems. 


176  THE    RATIONAL   ARITHMETIC. 

1.  Review  pages  98  and  99. 

2.  What  is  i  of  992  ? 

16,32  Change  9  hundreds  and  9  tens   to   8  hundreds 

ft\^QQQ  ^^^^  ^^  tens.      1^  of  8  hundreds  is  1  hundred. 

— - —  Change  19  tens  and  2  to  16  tens  and  32.     -J  of 

1-"^  16  tens  is  2  tens;   J  of  32  is  4 

3.  What  isyV«f  ^9^2? 

Chansre  59  hundreds   and  6  tens  to  55  hun- 


44,  22 
55,  46 


^  -i  \  ,^f^r>,^       dreds  and  46   tens.     -:rV  of  55   hundreds  is   o 
11) 5952       111 
hundreds. 

^^^  Change  46   tens  and   2  to  44  tens   and  22. 

-^  of  44  tens  is  4  tens ;  y^y  of  22  is  2. 

4.  What  is  J^r  of  7741  ? 

Change  77  hundreds  and  4  tens  to 
72,^^^  72  hundreds   and   54  tens.     J.-  of  72 

12)7741  hundreds  is  6  hundreds. 

645 1  xem.       Change  54  tens  and  1  to  48  tens  and 

61.     ^  of  48  tens  is  4  tens. 

Change  61  to  60.     -^.^  of  60  is  5. 
The  figure    that    is    left   over  in  an 
uneven  division,  as  the  1  here,  is  called 
the  remainder,  and    is    placed    to    the 
right  of  the  answer. 

5.  Divide: 

6)1764  7)2269  8)2936  6)2514  7)1624  8)3387 
9)2925  6)1318  7)2338  8)3656  9)8892  6)5544 
7)6475   8)7576  11)4631  10)2670   8)9352   9)3978 

9  -*       •      

12)2785  11)7857  10)4763   9)3565  10)5780  12)5256 
8)1032  11)7078  12)6888  11)8613   9)3288  12)8676 


PART   SECOND.  177 

1.  At  80^'  a  gallon,  what  is  the  value  of  one  quart? 

2.  How  many  years  do  1728  months  equal? 

3.  If  8  gallons  of  syrup  cost  §^12. 80,  what  does  1  gallon  cost? 

One  pint? 
•i.   A  boy  in  school  for  7  years  and  -t  montlis  studies  history 
during   one-eighth    of    the   time.      How   many   months 
does  he  study  history? 

5.  A  man  pays  $50  a  month  for  rent,  and  J  as  much  for  gas. 

How  much  does  he  pay  for  both? 

6.  A  grocer  sold  6  pounds  of  tea  for  $4.80.     How  much  did 

he  get  a  pound  for  it?     How  much  an  ounce? 

7.  A  person  bought  land  for  $4572,  he  sold  it  for  ^r  more 

than  it  cost;  for  how  much  did  he  sell  it? 

8.  How  many  cans  holding  5  pounds  each  can  be  filled  frojn 

2  hundredweights  of  coffee? 

D.   A  girl  divided  one-third  of   195   nuts   e(|ually   among  5 
friends.      How  many  did  each  re(;eive? 

10.  How  many  feet  long  is  a  platform  720  inches  long? 

11.  In  a  fire  a  man  lost  one- twelfth  of  his  goods,  all  of  which 

were    valued  at  $9,876.      How  many  dollars  worth  uii 
goods  did  he  lose? 

12.  A  farmer  owning   1,272  acres  of  land  divided  it  into  2 

equal  parts;  one  of  these  parts  he  again  divided  into  3 
equal   parts,  giving  one  of  these   parts   to  each  of  his 

3  sons,  and  keeping  the  rest  himself.     How  many  acres 
had  he  left?     How  many  acres  had  each  son? 

13.  A  book  case  contained  203  books,  each   of  the  7  shelves 

containing    the    same    number   of   books.      How^   many 

books  were  there  on  a  shelf? 
II.   A  man  sold  11  bicycles  for  $195.      They  were  all  sold  for 

the  same  price.     For  how  much  did  he  sell  each  one? 
15.   A  man  sold  9  horses  .iov  $783,  receiving  the  same  price 

for  each  one.     For  how  much  did  he  sell  each  horse? 


ITS 


THE   RATIONAL   ARITHMETIC. 


1. 
2. 
3. 
4. 

0. 

(). 

7. 

8. 

1). 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
11). 
20. 
21. 
22. 
23. 

24:. 

25. 
26. 


How  many  ^'s?     ^"s?     tV/^? 


What  part  of  O  =  A  ? 

AVliat  part  of  A  =  B  ? 

What  part  of  B  =  C  ? 

What  part  of  C  =  D  ? 

B  =  Avhat  ])art  of  O? 

C  =  wha,t  part  of  OV 

1)  =  what  ])art  of  O? 

How  many  A's  —  ()? 

How  many  B's  —  O? 

HoAv  many  O's  =  O? 

How  many  D's  =  O? 

In  1  how  many  4'sV 

What  part  of  1  is  4^  ? 

AYhat  part  of  4^  is  ^? 

What  part  of -J- is  |? 

What  part  of  I  is  J  ? 

AVhat  part  of  J  is  y\;  ? 

WJiat  part  of  |-  is  -/,.  ? 

What  part  of  l-  is  -^^^  ? 

J-  =  how  many  |'s?     How  many  -^'s? 

What  is  the  sum  of  I  and  ^? 

AVhat  is  the  sum  of  |-  and  J  ? 

What  is  the  sum  of  4,  \  ai]d  ^  ? 

What  is  the  sum  of  \  and  y\.  ? 

AVhat  is  the  sum  of  4 .  J,  \  and  y^g  ? 

Wliat  is  the  sum  of  \  and  -^^  ? 


1       'q9 

T  6  S  ' 


PART   SECOND.  179 


1.  E  is  what  part  of  O? 

2.  F  is  what  part  of  E?      What  part  of  O? 

3.  G  is  what  part  of  E?     Of  E?     Of  Oy 

4.  How  many  E's  =  O? 

5.  How  many  E's  —  O? 
().  How  many  O's  —  O? 

7.  In  1  liow  many  ^'sV      J's?     ^Vs? 

8.  .V  —  how  many  J.'s? 
1).    V  —  how  many  ^'s? 

10.  i  =  liow  manv  ,'.,'s? 

11.  1   z=i  liow  many  ,Vs? 

12.  AVhat  is  tlie  sum  of  ?,  and  I  ? 
in.    Wliat  is  the  sum  of  J  ami  ;.,  ? 
1-1.    Wliat  is  tlm  sum  of  J  and   ,'o  ? 
15.   What  is  tlio  sum  of  .l,  ,1  and  -,\,  ? 
If).   H  is  what  part  of  OV 

17.  I  is  what  pari  of  HV     What  part  of  O? 

18.  J  is  what  pari  of  I  V     Of  H  ?    Of  O? 
111.   How  many  H's  =  0? 

20.  Hi)w  many  T's  =^  O? 

21.  How  many  J's  =  O? 

22.  In  1  liow  many  J/s?     ^V's? 

23.  I  =  how  many  J,'s? 

24.  J)  =  how  many   iV'^^^ 

25.  J  =  how  many   /h's'i^ 
2f).    .',  =  how  many  /«'s? 

27.  I  =  how  many  tb'*^'^ 

28.  What  is  the  sum  of  J  and  ?,  ? 

29.  What  is  the  sum  of  J  and  -,^^^  ? 
80.  What  is  the  sum  of  i  and  yV? 

31.  What  is  the  sum  of  ^,  \  and  -^-^7 

32.  What  is  ^  of  i  ? 

33.  What  is  i  of  ^? 


18C  TDK  RATIONAL   ARITHMETIC. 

1.  What    is  the  weight    o£    4    packages  together,   the   first 

weighing  -J-  of  a  pound;  the  second,  ^  of  a  ponnd;  the 
third,  I  of  a  pound;  and  the  fourth,  1|  pounds? 

2.  A  tailor  uses  4^-  yards  of  chitli  for  a  coat;  If;   yards  for  a 

vest;  and  3^^^  yards  for  a  pair  of  trousei's.      How  many 
yards  does  he  use  for  the  suit? 
8.    A  man  sold  3  J  pounds  of  butter  to  one  customer,  2i  pounds 
to  another,  and  4|  to  a  third.      How  many  pounds  did 
he  sell  to  all  three? 

4.  A  lady  spends  i   of  the  year  in  the  city,  }  of  the  year  at 

the  seashore,  and  the  rest  of  the  year  in  traveling? 
AVhat  part  of  the  year  does  she  spend  in  traveling  ? 

5.  From  a  piece  of  cloth  15  yards  long,  8^-  yards  were  sold 

at  one  time  and  2 J  yards  at  another  time.     How  many 
yards  Avere  sold  in  all?     Hoav  many  yards  were  left? 
G.   A  baker  having   5   dozen  biscuits,  sold  14  dozen   to  one 
man,  and  2J   dozen  to  anotlier.      How  many  dozen  did 
he  sell  in  all?     How  many  had  he  left? 

7.  |-  of  John's  kite   string   is  whip-cord,  the  rest  is  cotton 

string  in  2  pieces,  the  first  piece  is  J  as  long  as  the 
whip-cord.  AVliat  part  of  the  entire  string  is  the  first 
piece  of  cotton  string  ?     Tlie  second  piece  ? 

8.  A  grocer  having  |   of  a  dozen   of  pineapples,  sold   l   of 

them.     What  part  of  a  dozen  did  he  sell? 
0.   One  boy  stays  in  the  country  ^  of  each  year,  a  second  boy 
stays   J    as  long  as  the  first  boy?     What  part  of  the 
year  does  the  second  boy  stay? 

10.  How  many  boxes  holding  \  of  a  pound  of  candy  each,  can 

be  filled  from  l-  a  ])ound?  From  |  of  a  pound?  From 
1^  pounds? 

11.  A  man  bought  1\  pounds  of  nuts  and  divided  them  equally 

among  his  4  children.  What  part  of  a  pound  did  each 
receive  ? 


PART   SECOND.  ISl 

1.  A  boy  bought  at  the  grocery  1  pound  of  sugar,  1^  pounds 

of  butter  and  -^  pound  of  tea.  How  many  ounces  did 
the  three  weigh  together? 

2.  A  man  bought  8 J  pounds  of  sugar  and  returned  12  ounces 

of  it.     How  many  ounces  did  he  keep? 

3.  A  grocer  put   5  pounds   of  sugar  into  2  equal  packages. 

How  many  ounces  in  each  package? 

4.  A  woman  bought  at  the  grocery  1|    pounds  of  butter  at 

24^  a  pound ;  a  quarter  of  a  pound  of  tea  at  60^  a 
pound  and  4  pounds  of  sugar  at  5|^  a  pound.  How 
much  is  her  bill? 

5.  A  clerk  sold  one  customer  7  yards  of  cloth  at  80^/  a  yard; 

9  yards  of  ribbon  at  l&f  a  yard  and  |  a  yard  of  velvet 
at  $1.50  a  yard.      AVhat  was  the  amount  of  his  sale? 

6.  A   man   bought  a  hatchet   for   75^.  a   saw   for   $1.25,  6|- 

pounds  of  ] jails  at  4^  a  pound,  and  2  dozen  screws  at  9^ 
a  dozen.      What  was  his  bill? 

7.  A  grocer  bought  3  barrels  of  sugar  containing  198  pounds 

each,  at  4^  a  pound;  a  box  of  tea  containing  23 
pounds  at  45^  a  pound,  and  2  sacks  of  coffee  containing 
75  pounds  each  at  20^  a  pound.     What  was  his  bill? 

8.  A  merchant  bought  3  dozen  pairs  of  shoes  at  $2.25  per 

pair,  one  dozen  at  $2.50  a  pair,  and  one-half  dozen  at 
$2.75  a  ])air.      How  much  was  his  bill? 

9.  A  bookseller  bought  50  books  at  S&f  each,  2  dozen  boxes 

of  paper  at  13^  each,  9  dozen  pencils  at  11^  a  dozen. 
What  was  his  bill  ? 
10.  Eailroad  fare  is  3^  per  mile.  From  Chicago  to  Aurora  it 
is  37  miles;  from  Aurora  to  Galesburg,  120  miles;  from 
Galesburg  to  Burlington,  43  miles.  What  is  the  fare 
from  Chicago  to  Aurora?  From  Aurora  to  Galesburg? 
From  Galesburg  to  Burlington?  What  is  the  fare 
from  Chicago  to  Burlington? 


182  THE   RATIONAL   ARITHMETIC. 

1.  A  man  oavijs  a  lot  ou  wliicli  ho  builds  2  houses.     The  first 

is  244^  feet  wide  and  68  feet  knitj^;  the  second  is  25 
feet  wide  and  ()2l  feet  long.  AVliat  is  the  area  of  tlie 
ground  covered  hy  the  two  houses  V 

2.  The  lot  is  125  feet  long  and  ()0  feet  wide.      What  is  the 

area  of  the  ijround  not  covered  ])V  tlie  houses? 

3.  A  street  is  i)()()   feet  Jong   and  (>()   feet  wide;  there  is  a 

sidewalk  7  feet  wide  on  each  side.  What  is  the  area  of 
the  remainder  of  the  street? 

4.  A  railroad  runs  a  train  of  3  cars  e\er)'  30  minutes  from  (J 

o'clock  ill  tli(!  morning  until  <>  in  the  evening.  How 
many  cars  run  over  the  track  in  the  12  hours? 

5.  A  man  mails  40  letters  requiring  2^/   postage  each,  375 

circulars  requiring  1^/-  postage  cjicIj,  and  30  [)ackages 
Avhich  require  4^/-  each.  What  is  the  cost  of  the  postage 
on  the  whole? 
0.  A  man  subscribed  for  the  Youth's  Com[)anion  for  one 
year  at  $1.75,  for  St.  Nicholas  for  6  months  at  $2.50  a 
year,  for  the  Century  for  3  months  at  $4  a  year  and 
for  McClure's  for  18  months  at  $1  a  year.  How  much 
must  he  pay  for  all  the  subscriptions? 

7.  A  boy  bought  24  1-cent  papers  at  j^  each,  16  2-cent  papers 

at  1^^  each  and  5  10-cent  magazines  at  7^  each.  He 
sold  his  entire  stock  at  regular  prices.  How  much 
money  did  he  make? 

8.  A  boy  gets  $3.75  for  a  week's  work;    lie  pays  10^  each 

day  for  lunches,  buys  a  ball  for  15^/  and  a  stamp  album 
for  75^.  How  much  money  does  he  have  left  at  the 
end  of  the  week? 

9.  A  man  gets  $17.50  a  week  for  four  weeks.      In  that  time 

he  pays  $11  for  rent,  buys  half  a  ton  of  coal  at  $7.50  a 
ton,  pays  $12.75  for  groceries  and  $().03  for  dry  goods. 
How  much  money  has  he  left  from  his  salary? 


PART   SECOND.  183 

1.  48  men  dig  a  celhir  in  IS  days.     In  how  many  days  could 

12  men  liave  dui;  itV 

2.  How  many  ^-pound  [)ackages  can  be  made  from  18  chests 

of  tea,  each  containing  60  pounds? 

3.  How  many  pounds  of  sugar  at  G^  a  ])ound  will  0(pial  iji 

value  258  gallons  of  syrup  at  4(K/  a  gallon? 

4.  A  merchant  exchanged  70  barrels  of  sugar  at  .S22.')0  p(;r 

l)arrel  for  flour  at  §5  per  barrel.  How  many  ])arrels  of 
flour  did  he  receive? 

5.  If  250  desks  which  cost  $0  each  are  sold   for  §12  each, 

what  will  be  the  gain? 
<).   AVliat  will  144  quarts  of  strawberries  cost  at  50^/  a  peck? 

7.  What  is  the  difference  between  829  tons  and  -^.^  of  9b48 

tons  ? 

8.  Mr.  Monroe  s[)ends  i^l39.<J5  in  .lanuaiy,  ^:>15.25  more  in 

Februarv  than  in  Jfuiuarv,  and  $15.25  more  in  March 
than  in  February.     How  much  does  he  spend  in  all  ? 

9.  A   gentleman   paid  for   a   ])urchase   with   a   $5   bill,   mikI 

received  back  in  change  one  half-dollar,  8  qunrters,  2 
dimes  and  2  nickels.  What  was  the  amount  of  his 
change?     What  was  the  amount  of  his  purchase? 

10.  Find  the  distance  in  inches  around  a  room  that  is  18  feet 

long  and  14|  feet  wide. 

11.  A  woman  received  §10,000  for  a  farm.      She  gave  $10(M) 

to  a  church,  $500  to  a  school,  and  §2980  to  a  hospital. 
How  much  of  the  money  had  she  left? 

12.  A  carpenter  bought  464  feet  of  lund^er  at  cme  time  and  ^ 

as  much  at  another  time.  How  many  feet  did  he  bu}' 
in  all? 

13.  There  are  387  squares  of  marble  in  the  floor  of  the  dining- 

room  and  seven-ninths  as  many  in  the  parlor  floor. 
How  many  squares  in  the  parlor  floor?  How  many  in 
both  floors? 


184  THE   RATIONAL  ARITHMETIC. 

1.  A  man  paid  $24  for  a  suit  of  clothes,  -J  as  much  for  a  pair 

of  shoes,  J  as  much  for  a  hat.  What  was  the  cost  ol 
the  entire  outfit? 

2.  A  man  paid  for  his  house  $48(50;  the  h)t  cost  him  J  as 

much  as  the  house;  the  grading,  fencing  and  street 
cost  J  as  much  as  the  lot.      WJiat  did  the  three  cost  him? 

3.  A  bookseller  sold  $128  worth  of  hooks  in  one  day.      They 

cost  him  L  less  tlnm  he  sold  them  for.  How  much  was 
liis  profit  and  what  did  the  books  cost  iiim  ? 

4.  A  bookseller  sold  64  books  at  12^^/  each,  48  ])ooks  at  15</' 

each,  and  (50  books  at  25</'  each.  How  much  money 
did  he  receive? 

5.  There  are  60  pupils  in  the  school  room.      24  of  them  have 

4  books  each,  26  of  them  have  S  books  each,  and  the 
remainder  have  5  books  to  each  group  of  2  pupils. 
How  many  l)ooks  are  thei-e  in  the  room  ? 

6.  A  man  is  48  years  old;  his  wife  is  44;  the  oldest  son  is 

^  as  old  as  the  father  and  mother  together;  the  second 
son  is  J  as  old  as  the  father.  What  is  the  sum  of  the 
ages  of  the  father,  mother  and  two  ])oys? 

7.  A  boy  left  home  for  college  on  the  morning  of  Septem- 

ber 5th.  He  returned  home  on  the  morning  of  Decem- 
ber 28rd.     How  many  days  was  lie  away  from  home? 

8.  A  family  bought  1   (|uart  of  ]nilk  every  day  in  January, 

February  and  March  of  a  Lea[)  Year.  How  many  gal- 
lons did  tliey  buy  in  the  8  montiis? 
0.  For  $20  in  gold  a  man  received  a  five-dollar  bill,  7  silver 
dollars,  and  the  rest  equally  in  half  dollars  and  quar- 
ters. How  many  half  dollars  did  lie  get?  How  many 
quarters  ? 
10.  How  many  yards  of  wire  are  needed  to  build  a  fence  six 
wires  high  around  a  garden  48  feet  wide  and  72  feet 
long? 


PAK'I'    THIRD. 

1.  Measure   tliese   two   lines.      Suppose   theui   to   be 
drawn  to  the  scale  of  i  inch  to  8  feet. 

2.  What  does  the  short  one  represent? 

3.  How  many  times  the  short  line  is  the  lontr  one? 

4.  If  the  short   line   represents   1   yai'd,   how   many 
yards  does  the  long  one  represent? 

5.  If  the  short  line  represents  3  feet,  how  many  feet 
does  the  long  one  represent? 

6.  We  will  call  the  long  line  1  rod. 

7.  How  many  feet  in  a  rod? 

8.  How  many  yards  in  a  rod? 

9.  How  many  feet  in  a  yard? 

10.  How  many  inches  in  a  foot? 

11.  320  times  what  the  long  line  represents  is  a  mile, 

12.  How  many  yards  in  a  mile? 

13.  How  many  feet  in  a  mile? 

14.  How  many  rods  in  a  mile? 

15.  A  boy  walks  00  rods.     How  many  yards  does  he 
walk?     How  many  feet? 

16.  A  lot   6  rods  wide  is  divided  into  2   equal    lots. 
How  many  feet  wide  is  each  lot? 

17.  A  lot  is  3  rods  wide  and  G  rods  long.     How  many 
yards  around  it? 

18.  A  bridge  is  8  rods  long  and  2  rods  wide.     How 
many  feet  long  and  wide  is  it? 

19.  A  rope  12  rods  long  is  wound  into  coils,  each  coil 
using  6  feet  of  rope.     How  many  coils  are  there  ? 

I  20.   How  many  rods  around  a  farm  2  miles  square? 

185 


1  foot 

1  yard 

1  rod 

12  inches 

3  feet 

5}4  yai'ds 

30  inches 

lek  feet 

ISO  THE   RATIONAL   x\RITHMETlC. 

1  mile 
320  rods 
1700  yards 
5280  feet 

1.  A  ])look  is   18   rods  wide  and  2'2  rods  long.      How  many 

vai-ds  is  it  M)-onnd  tli«^  l)lo(dvV     How  many  IVetV 

2.  A  hoy   lives   1)4:   i<k1s    from   school.      it*  ho  goes   home  at 

noon  how  many  yards  does  lie  travel  in  a  school  week? 

3.  A  man  lives   2 A    miles   from   his  office.      He   ifoe»  to  his 

office  each  day.      How  many  rods  does  he  travel  from 
Monday  moi-ning  nntil  Saturday  night? 

4.  A  lot  is  82J   feet  wide  and  105  feet  long:.      What  is  the 

cost  of  fencing  it  at  18^/  a  yard?     At  75^'  a  rod  ? 

5.  'I^lie  I'ails  on  a  railroad  are  2  rods  long.      How  many  rails 

are  there  in  a  mile  of  railroad  track? 
().    It  costs  Hy>(/-  a  linea]'  foot  for  making  a  street.     What  will 
])e  tlie  cost  of  a,  ([iiMi'ter  of  a  mile  of  such  a  street? 

7.  A  ))oy  I'ode  7^   miles  on  his  wheel.      How  many  rods  did 

he  ride? 

8.  It  is  HS  yai'ds  west   from    the   door  of  Jolm's  house  to  the 

schooh      If  he  went  to  tlie  store  45  yards  east  and  then 
to  school,  how   many  yards  did   he  walk?     How  many 
feet? 
1).   How  many  yards  of  border  will  be  required  for  a  room  21 
feet  long  and  18  feet  wide? 

10.  The  tire  of  a  wheel  measures  Ct  feet.      How  many  revolu- 

tions will  it  make  in  going  24  rods? 

11.  A  boy  steps  2  feet.     How  many  yards  will  lie  stej)  in  80 

steps?     How   many   steps   will    he   take   in   Avalking  a 
mile?     In  walking  %  a  mile?     In  walking  ^  of  a  mile? 

12.  If  there  are  8  blocks  in  a  mile,  how  many  feet  ai'e  thei'e 

in  a  block ? 
18.   A  field  is  ^  a  mile  square.      How   many   miles  will  a  man 
travel  in  going  around  the  field? 


PART   THIRD.  18^^ 

A B C 

1.  This  line  is  drawn  to  a  scalo  oC  1  iiicli  to  i\w,  mile.     A 

man  ij^oes  from  C  to  A  find  returns  to  U.  How  njajiv 
miles  lias  he  traveled? 

2.  From  B  he  s^oes  to  C  and  returns  to  B.    How  many  miles 

has  he  traveled? 

3.  From  B  he  goes  to  A  and  back  to  B.      How  many  rods 

has  he  traveled? 
J:.   Suppose  the  line  to  be  drawn  to  a  scale  of  I)  rods  to  1 
inch.      How  many  yards  from  A  to  B?     From  B  tt^  C? 
From  A  to  C  ? 

5.  John  lives  at  B,  Ned  at  A  and  the  school-house  is  at  C. 

John  goes  to  Ned\s  house  in  the  morning,  then  to 
school,  and  home  in  the  evening.  How  many  rods  has 
he  traveled? 

6.  The  next  day  Ned  goes  to  school  and  Jolin  is  not  there. 

He  i^oes  back  to  John's  home  and  they  <n)  back  to 
school  together  and  each  returns  home  in  the  evening. 
How  many  rods  has  Ned  traveled?     How  many  yards? 

7.  Let  each  boy  count  the  number  of  steps  to  his  home  from 

school,  write  it  down  and  the  next  day  find  how  many 
feet  the  distance  is  if  his  steps  have  been  2  feet  long. 
If  he  steps  14  feet.  Tell  whether  it  is  nearer  a  mile, 
i  a  mile,  ^  of  a  mile  or  ^  of  a  mile. 

8.  How  many  feet  in  -|  a  mile?     ^  of  a  mile?     J  of  a  mile? 

y.  2  boys  start  out  from  home  and  walk  in  opposite  direc- 
tions. They  take  8  steps  to  the  rod.  How  many  rods 
apart  are  they  when  they  have  each  taken  80  steps? 

10.  Is  the  distance  they  are  apart  nearest  to  ^,  ^  or  to  a  mile  ? 

11,  A  boy  takes  80  steps  of  2  feet  each  in  a  minute.      How 

far  will  he  walk  in  15  minutes?  Is  the  distance  nearer 
to  ^  or  J  a  mile? 


188 
A 


THE   RATIONAL   ARITHMETIC. 


B 


D 


G 


The  above  is  a  map  of  a  country  road  starting  from  the  street  A — X, 
M»d  drawn  to  a  scale  of  one  inch  to  four  miles. 

1.   How  many  miles  is  it  from  the  street  to  B?    To  D?    To  G? 
"2.   How  many  miles  is  it  from  B  to  G?     From  D  to  G? 
S.  How  far  is  the  road  B  C  from  the  street  ?     How  far  is  1)  E  ? 
'  4.  How  far  is  the  road  F  G  from  the  road  D  E? 

5.  How  far  is  the  road  F  G  from  the  street? 

6.  How  far,  in  a  straight  line,  is  the  road  A  B  from  the  road 

F  E? 

7.  How  far  is  the  end  of  the  road  at  G  from  the  nearest  })oint 

of  the  street? 

8.  How  far  is  G  from  the  nearest  point  in  the  road  A  B? 

9.  The  distance  from  B  to  0  is  what   part  of  the  distance 

from  F  to  G?     What  part  of  D   to  E?     What  part  of 
C  to  D?     What  part  of  A  to  B?    What  part  of  D  to  F? 

10.  The  distance  from  F  to  G  is  what  part  of  the  distance  from 

A  to  B  ?     What  part  of  the  distance  from  D  to  E  ? 

11.  The   distance   from   0  to  D  is  what  part  of  the  distance 

iroiu  A  to  B  ?  _  What  part  of  the  distance  from  F  to  G  ? 


PART   THIRD.  180 

(Call  one  inch  on  the  map  one-half  a  mile.) 

1.  How  far  is  it  from  A  to  B?     From  A  to  C?     From  A  to 

D  ?     From  B  to  C  ?     From  E  to  F  ?     From  E  to  G  ? 
(Call  one  inch  on  the  map  one-third  of  a  mile.) 

2.  How  far  is  it  from  A  to  B  ?     From  A  to  C  ? 

3.  If  a  man  can  walk  from  A  to  B  in  15  minutes,  how  Ions: 

Avill  it  take  him  at  the  same  rate  to  walk  from  D  to  EV 

4.  If  the  wheels  of  a  bicycle  turn  twice  around  in  going  one 

rod,  how  many  times  will  they  turn  in  going  six  miles? 

5.  John  starts  on  his  bicycle  and  rides  IJ  miles  in  8  minutes; 

Harry  rides  at  the  same  speed  for  5  minutes.  How 
many  more  rods  does  John  ride  than  Harry? 

6.  There  are  in  a  room  5  windows  9  feet  high.     How  many 

yards  of  material  of  single  width  will  be  required  to 
make  curtains  for  the  windows,  making  2  curtains  for 
each  window?     What  will  be  the  cost  at  6^-  a  yard? 

7.  The  windows  in  a  school  room  are  7  feet  high  and  there 

are  4  of  them.  How  many  yards  of  material  will  be 
required  for  one  curtain  at  each  window  if  1  foot  is 
allowed  extra  for  each  curtain  ?  AVhat  will  be  the  cost 
of  the  material  at  25^  a  yard? 

8.  Each  step  in  the  staircase  is  6  inches  high  and  1  foot 

wide.  How  many  feet  of  stair  carpet  will  be  required 
if  there  are  12  steps?  AYhat  will  be  the  cost  of  the 
carpet  at  75^  a  yard? 

9.  In  a  library  35|  feet  long  and  23|  feet  wide,  there  are 

book  shelves  on  one  side  and  one  end  of  the  room.  How 
many  feet  of  boards,  in  length,  will  be  required  to 
make  5  of  these  shelves? 
10.  A  pile  of  10  blocks  is  placed  6  yards  from  a  basket.  If  a 
child  starts  at  the  blocks  and  carries  1  at  a  time  to  the 
basket  until  he  has  carried  all  the  blocks,  and  returns, 
how  far  will  he  have  walked? 


100 


THE   RATIONAL   ARITHMETIC. 


1. 


12^2 

1 

2 

3 

4 

D 

G 

7 

Vdcl:^ 

12i 
12| 
12.V 


12^  X  2  = 

124:    X    3    :rr 
12i    X    4   rr: 

121  X  5  =. 

25  X  2  =  _ 
25  X  3  =  _ 
25  X  4  =  _ 
50   X   2  =:  - 


12i 
121 
12?. 


1^4- 
12|- 

121 
121 


1*4 
12| 
121 
12X 

121 

12^ 


Of  50?     Of  75? 


12>2 
25 

37)^ 

50 

62^2 
75 

87 1/2 

TOO 

12i 
121 
121 
121 
121- 
121- 

2 

191 


121  X  6  = 
12I  X  7  - 

121  X  8  ^ 

25  -  121  = 
50  -  121  = 
75  -  12^  =: 
100  -  12^  = 
Of  100?"" 


4.  25  is  what  part  of  50?     Of  75? 
50  is  what  part  of  75?     Of  100? 
75  is  what  part  of  100? 

5.  121  jg  ^yiiat  part  of  25  ? 
121  is  what  part  of  100? 

6.  How  many  timos  12?,  is  371?     024  ?     871? 

7.  What  part  of  100  is  37^-?     62^?     87|^? 


12* 
121 

12* 

12* 

12* 
12* 

12* 
121 


PART   THIRD.  191 

1.  A  woman  sold  4  dozen  eggs  at  124^'  a  dozen.     How  much 

did  she  get  for  them  ? 

2.  What  is  the  cost  of  5  pounds  of  butter  at  12^^-  a  pound? 

3.  How  many   12^^'  in  a   dollar?     In  J  of  a  dollar?     In  a 

half  dollar?  ''in  75^? 

4.  A  hoy  bought  a  dozen  little  chickens  at  12t\^-  each.     The 

feed  cost  him  75^'  and  he  sold  the  chickens  when  they 
were  grown  at  25^'  each.  How  much  did  he  make  in 
the  chicken  business? 

5.  A  farmer  hired  a  boy  to  watch  his  corn-field  and  prom 

ised  him  12-|^  for  every  3  squirrels  and  12^^-  for  every 
5  crows  that  he  killed.  At  the  end  of  a  week  the  boy 
turned  in  6  squirrels  and  10  crows.  How  much  money 
should  the  farmer  pay  him  ? 

6.  A  woman  bought  10  yards  of  ribbon  at  12|Y'  ^  yard  and  8 

yards  of  silk  at  87^^/  a  yard.  What  was  the  cost  of  the 
ribbon?     Of  the  silk?     Of  both  together? 

7.  A  boy  bought  a  ball  for   12^^;,  a  bat  for  25^-  and  a  glove 

for  37iY'.  How  much  did  he  pay  for  his  base-ball 
outfit?" 

8.  A  girl  bought  a  doll  for  25^',  a  tablet  and  pencil  for  12^^' 

and  a  book  for  37i^'.  How  mucli  change  should  she 
receive  if  she  gave  the  storekeeper  5^1? 

9.  A  book-seller  bought  5  books  at   127^^-  each,  8  boxes  of 

paper  at  12^(/;  each  and  7  dozen  pencils  at  12^^  a 
dozen.     What  was  the  cost  of  the  whole? 

10.  A  hall  is  12i  feet  wide  and  C  times  as  long.     How  long 

is  it? 

11.  A  board  is  12^-  inches  wide  and  7  times  as  long.     How 

many  inches  long  is  it? 

12.  A  boy  bought  3  dozen  eggs  for  |  of  a  dollar,  and  sold 

them  for  J  of  a  dollar.  What  part  of  a  dolhir  did  he 
gain?     How  many  cents  a  dozen  did  he  gain? 


192  THE   RATIONAL   ARITHMETIC. 

1.  A  clerk  sold  1  piece  of  silk  cord  4J  feet  long,  another  7^ 

feet  long.      How  many  yards  did  lie  sell  in  all  ? 

2.  A  man  wishes  to  put  2  rows  of  wire  above  a  fence  12  rods 

long.     How  many  feet  of  wire  does  he  need  ? 

3.  How  many  yards  of  carpet  are  needed  to  lay  one  width 

in  a  hall  224-  feet  long  and  on  a  fliofht  of  16  stairs,  each 
step  requiring  1-|  feet  of  carpet? 

4.  John  rides  12  miles,  his  brother  f  as  far.     How  many 

rods  does  his  brother  ride? 

5.  A  field  is  160  rods  long  and  80  rods  wide;  how  many 

feet  of  wire  will  enclose  it  twice  ? 

6.  A  man  left  home  and  drove  5  miles  east ;  turned  and  drove 

1,000  rods  back.      How  far  was  he  from  home? 

7.  The  hall  of  a  hotel  is  14  yards  long  and  16^  feet  wide. 

How  many  feet  of  border  will  be  required  to  go  around 
the  walls? 

8.  How  many  boards  12  feet  long  will  make  a  fence  1  mile 

long,  if  there  are  3  rows  of  boards? 

9.  One  walk  is  150  feet  long,  a  second  80  feet  long,  and  a 

third  240  feet.  What  is  the  length  in  yards  of  all 
together? 

10.  One  rail  of  a  track  is  30  feet  long.    How  many  miles  long 

is  a  track  having  on  1  side  352  rails,  each  30  feet  long? 

11.  A  street-car  company  lays  7  miles  of  track,  J  of  it  running- 

east  and  west,  the  rest  north  and  south.  How  manv 
rods  of  track  are  there  in  all  ?  How  many  running 
each  direction? 

12.  A  boy  walked  2  miles,  taking  steps  2  feet  long.     How 

many  steps  did  he  take? 

13.  In  building  a  fence  around  a  field  |  of  a  mile  long  and  \ 

of  a  mile  wide,  a  farmer  used  old  material  for  2,250 
yards,  and  purchased  the  rest.  How  many  yards  of 
fencing  did  he  buy  ? 


PART   THIRD.  19 


Q 


1.  A  horse  can  go  1  mile  in  6  minutes.     How  many  rods 

can  lie  go  in  an  hour? 

2.  A  carriage  wheel  measures  12  feet  around  the  outside. 

How  many  times  will  it  turn  around  in  going  3  miles? 
In  going  5  miles? 

3.  A  wheel  is  10  feet  around  the  outside.     How  many  yards 

will  it  move  in  going  around  120  times  on  the  ground? 

4.  A  lot  is  23  yards  wide.     How  many  rods  will  a  man  walk 

in  crossing  the  lot  8  times? 

5.  A  boy's  top-string  is  2  yards  long,  he  cuts  from  it  a  piece 

18  inches  long.  AVhat  is  the  length  in  feet  of  the 
remaining  part? 

6.  A  mile  of  gas  pipe  is  laid  at  $5  a  rod.     AVhat  is  the  cost 

of  laying? 

7.  A  ])lock  is  18  rods  wide  and  24:  rods  long.     How  many 

steps  of  2  feet  in  length  will  a  boy  take  in  going  around 
it  once? 

8.  A  street  car  goes  10  miles  in  an  hour.     At  the  same  rate, 

how  many  rods  will  it  go  in  15  minutes? 

9.  At  25^'  a  foot,  what  will  be  the  cost  of  4:  rods  and  1  foot 

of  hose? 

10.  A  boy  starts  from  his  home  and  takes  80  steps  of  2  feet 

each  in  a  minute.  He  walks  at  that  rate  as  far  as  he 
can  go  and  return  in  10  minutes.  How  far  Avas  he 
from  home  when  he  turned  to  go  back? 

11.  A  man  walked  4  miles  an  hour  and  a  boy  walked  2  miles 

an  hour.  They  started  in  the  same  direction  at  the 
same  time.  How  many  rods  apart  were  they  in  15 
minutes  ? 

12.  AYhat  Avill  be  the  cost  of  a  ditch  half  a  mile  long  at  $1.25 

a  rod? 

13.  What  is  the  distance  around  a  lot  which  is  50  yards  and 

2  feet  long  and  8  yards  and  1  foot  wide  ? 


194 


THE   RATIONAL  ARITHMETIC. 


1.   Give  the  iiuml)or  of 
12's  ill 

r 


8. 


24       30 
42     144 

18  132 
96  ()0 
48  36 
12  X  4  =  . 
12  X  1)  =  . 
12  X  7  =  - 
12  X  10  =  . 
12  X  8  =  _ 
12  X  2^,  =  _ 
12  X  51  3-  - 


84 

m 

108 

72 

120 


12  X 
12 


12  X  83.  = 


12  X 
12  X 


f — 
12 

24 

10 

18 
9 
5 


3  J    • 
s  m 

L_ 


ITf 


() 
27 
22 
30 

27 


36 
15 
21 
14 
33 


3  = 


12  X  12  = 
12  X  6  r- 
12  X  11  = 

12  X  101  ^ 

12  X 

12  X     31 


'^\^ 


12  X  121  ... 


12  X 


^ 


4.   h\  is  wliat  })aTt  of  11?     What  })art  of 


5. 


T'  1 


X  2    := 

5J-    X  4    := 

51  X  7  = 

51  X  8  =- 


51  X  6  =  - 
51  X  9  -  - 
54^  X  3  =  _ 
51x10=  - 

6.  \  of  320  ^ 
1  of  320  = 

J^  of  320  = 

7.  2  X  320  =  . 
5  X  320  =  . 


16^  X  3 

16^-  X  (i 

l4  X  4 

161  X  2 
161  X 

i4x 

164:  X     \\ 
X 


161 


92 


77 

00 

132 

m 

88 

3  X  11  -  - 

3  X  12  =  . 

3  X  5  :=  . 

3  X  8  rr  . 

3  X  \)  ^  - 


S  111 

110 
99 
33 

121 
44 


3  X  8<   = 


51=. 
1   — 


3  X 

3  X  9^  == 
3  X  121  ^  _ 
l()i?  Of  22? 
ll  X  8  =  _ 
11  X  9  -=  _ 
11  X  12  -:  - 
11  X  4  =  - 
11  X  7  =  - 
11  X  10  =  - 
11  X  6  =  - 
11  X  11  =  - 


4 


of  320 
Vg  of  320 
-3V  of  320 

3  X  320 

4  X  320 


a.  What  part  of  320  is  40?     AVhat  part  is  80?     20? 


PART   THIRD.  195 

1.  If  1  cord  of  wood  cost  ^5t\,  how  much  will  4  cords  cost? 

2.  How  many  12  pound  packages  of  sugar  can  be  made  from 

72  pounds? 

3.  How  many  bins  holding  ^h  bushels  can  be  filled  from  IG^ 

bushels  of  grain  ? 

4.  A  man  walked  IGJ  miles  1  day  and  bfy  miles  the  next. 

How  many  miles  did  he  walk  in  all?     How  many  miles 
farther  the  first  day  than  the  second? 

5.  At  |5|  a  ton,  how  many  tons  of  coal  can  be  bought  for 

$22"? 
0.   11  men  received  $132  for  digging  a  ditch.     They  shared 
the  money  equally.      What  did  each  one  receive? 

7.  A  farmer  bought  10  sheep  at  $3  each  and  sold  them  at 

the  rate  of  3  for  $12.     What  was  the  entire  cost?    How 
much  did  he  receive?     AVhat  was  his  gain? 

8.  A  flag  staff  48  feet  high  was  broken  into  2  pieces,  1  piece 

being  3  times  as  long   as  the  other.      What  Avas  the 
length  of  each  piece? 

9.  What  is  the  cost  of  a  bale  of  cotton  containing  400  pounds, 

at  5^^'  a  pound?     At  7^/  a  pound? 

10.  From  a  bin   holding  77   bushels,  55  Inishels  were  taken 

out.     How  many  bins  holding  5|  bushels  each  can  be 
filled  from  the  remainder? 

11.  $40  a  month  is  paid  by  a  man  for   his   rent;    his   other 

monthly  expenses  are  7  times  as  much.     What  is  the 
amount  of  his  other  expenses?     Of  total  expenses? 

12.  A\^hat  is  the  average  rate  of  speed  made  by  a  train  travel- 

ing 320  miles  in  8  hours? 

13.  A  grain  dealer  sold  320  bushels  of  corn  in   40   bushel 

loads.     How  many  loads  did  he  sell? 

14.  A  bushel  of  wheat  weighs  4  pounds   more  than  a  bushel 

of  corn.     What  is  the  difference  in  weight  between  80 
bushels  of  each? 


196  THE   RATIONAL  ARITHMETIC^ 

1.  Draw  diagrams  on  a  scale  of  3  feet  to  1  inch  for  Tooms 

of  the  following  dimensions: 
12  feet  long  and  9  feet  wide. 
24  feet  long  and  18  feet  wide. 
30  feet  long  and  27  feet  wide. 
33  feet  long  and  21  feet  wide. 
15  feet  long  and  12  feet  wide. 
21  feet  long  and  12  feet  wide. 
27  feet  long  and  15  feet  wide. 
24  feet  long  and  15  feet  wide. 
Give  perimeters  in  feet.     In  yards. 

2.  Draw  diagrams  on  a  scale  of  3  yards  to  1  inch,  for  lots  of 

the  following  dimensions: 
15  yards  long  and  12  yards  wide. 
18  yards  long  and  15  yards  wide. 
12  yards  long  and  G  yards  wide. 
15  yards  long  and  9  yards  wide. 
24  yards  long  and  12  yards  wide. 
33  yai'ds  long  and  15  yards  wide. 
21  yards  long  and  12  yards  wide. 
27  yards  long  and  12  yards  wide. 
Give  perimeters  in  yards.     In  feet. 

3.  Draw  diagrams  on  a  scale  of  J  mih^  to  |-  inch,  for  fields 

of  the  following  dimensions: 
I  mile  long  and  \-  mile  wide. 

1  mile  long  and  |-  mile  wide. 

2  miles  lono^  and  l.V  miles  wide, 
li  miles  lonof  and  .V  mile  wide. 
1\  miles  long  and  1  mile  wide. 
1^  mile  long  and  -\  mile  wide. 

li  miles  long  and  |  mile  wide. 
1\  miles  long  and  l  mile  wide. 
Give  perimeters  in  miles.     In  rods. 


PART    THIRD.  197 

1.  Review  page  176. 

2.  When  dividing  by  numbers  larger  than  12,  the  changes 

may  more  easily  be  written  below  the  numl)er,  as  shown 
in  8.  This  way  of  dividing  is  called  Long  Division, 
but  the  plan  is  the  same  as  in  Short  Division. 

3.  Divide  559  by  13. 

Change  55  tens  and  9  to  52  tens  and  39;  write 

^3     the    52    tens    below    the    55,    draw    a    line,   and 

13 j  559     beneath   it  write  the  39,  placing   tho   3   tens  in 

'^'^        tens'  column. 

39  Now  divide :  52  tens  -^  13  ==  4  tens ;  39  -J- 13  =  3, 

39     making  the  answer   43.       Write    this    above  the 

559,   placing  each    figure  in  its  proper  column, 

the  4  tens  above  the  5  tens,  the  3  above  the  9. 

4.  Divide  4874  by  21. 

Change   48   hundreds  and   7   tens  to  42 
232-^1-       hutidreds  aud  07  tens;    write  the  42  hun- 
21)4874  dreds  below  the  48,   draw   a   line,   and  be- 

42  neath   it  write   the  67  tens,   placing  the  6 

67  hundreds  in  hundreds'  column. 

63  Now  divide:    42  hundreds  -^  21  =  2  hun- 

44  dreds.      Place  this  part  of  the  answer  above 

42  the  4,874,  in  hundreds'  column.    Change  67 

2-rem.   tens  and  4  to  63  tens  and  44,  writing  them 
in  the  same  way  as  before. 
Now  divide:   63  tens  -4-  21  =  3  tens.     Write  this  part  of  the 
answer  in  its  proper  column,  beside  the  4  hundreds. 

Change  the  44  to  42  and  2.      42  -^  21  =  2.     Write  this  in 
the  ones'  column  of  the  answer. 

The  division  of  the    remainder,   2,   may    be    expressed    by 
writing  ^  after  the  rest  of  the  answer,  making  232/y. 


198  THE   RATIONAL   ARITHMETIC. 

1.  Divide: 

264  by  11,  by  21,  31,  41,  51. 
528  by  12,  by  22,  32,  42,  52. 
377  by  13,  by  23,  33,  43,  53. 
434  by  14,  by  24,  34,  44,  54. 
675  by  15,  by  25,  35,  45,  55. 
352  by  16,  by  26,  36,  46,  56. 

2.  Divide   each   of   the   followiug   iiuinbers    by   each  of  the 

above  series. 


118 

154 

172 

120 

156 

188 

213 

237 

248 

253 

269 

293 

3123 

3234 

3345 

3456 

3567 

3785 

4678 

5788 

6879 

7890 

8901 

8493 

9012 

8123 

7243 

6542 

5987 

9648 

3.  A  mail  })aid  ^31.46  for  egg^  at  13</  a  dozen.      How  many 

dozen  did  lie  buy? 

4.  A  tank  holds  300  barrels  of  water.      When  it  is  y^g  full, 

how  many  barrels  does  it  hold?     How  many  gallons? 

5.  In  a  flock  of  1,736  sheep,  j\  of  the  •number  were  lambs. 

How  many  lambs  were  there? 

6.  A  man  bought  20  feet  of  piping  for  $6.40.      How  much 

per  foot  did  it  cost?     How  much  per  inch? 

7.  A  man  bought  18  yards  of  cloth  for  §3(3.72.     How  much 

did  it  cost  a  yard? 

8.  A  man  bought.  25   pictures,  paying   for   thein   $925.      If 

each  one  cost  the  same,  Avliat  was  the  cost  of  one  picture? 

9.  A  grocer  sold  19  pounds  of  butter  for  Avhich  he  received 

$4.37.     How  much  per  pound  did  he  get? 

10.  A  boy  can  ride  15  miles  an  hour  on  his  bicycle.     At  the 

same  rate  how  many  hours  would  it  take  him  to  ride 
5,136  miles? 

11.  The  schoolroom  floor  contains  1,100  square  feet  and  is  25 

feet  wide.     How  long  is  it? 


PART   THIRD.  199 

1.  A  grain  dealer  sold  (365   bushels  of  oats  in  loads  of  35 

bushels  each.     How  many  loads  did  he  sell? 

2.  A  man  j)aid  e§71J.58  for  butter  at  23^  a  pound.    How  many 

pounds  did  ho  buy? 

3.  A  lot  contains  4,232  square  feet  and  is  23  feet  wide.    How 

lon«r  is  it? 

4.  If  24  horses  cost  $1,080,  what  is  the  average  cost  of  one? 

5.  3,300  bushels  of  grain  were   put   into  22  bins  of  equal 

size.      How  many  bushels  in  each  bin? 

6.  In  laying  a  railroad  1,200  miles  long,  one- sixth  of  it  was 

built  over  hilly  ground,  and  one  twenty-fourth  of  it 
over  water,  the  rest  ran  over  level  ground.  How  many 
miles  of  railroad  in  each  part? 

7.  If  there  are  40  single  seats  in  each  room  in  a  schoolhouse, 

how  many  rooms  will  be  needed  to  seat  1,680  pupils? 
To  seat  8,640  pupils? 

8.  A  merchant  bought  2   dozen   pairs  of  shoes   for  $52.80. 

How  much  did  he  pay  a  pair? 

9.  How  many  ponies  at  $50  each  can  be  bought  for  $1,000? 

10.  A  bookseller  bought   1,485   books.      They  were  packed  in 

15  boxes  with  an  equal  number  in  each  box.  How 
many  books  were  there  in  each  box? 

11.  A  coal  dealer  shipped  2,916  tons  of  coal  in  cars  of  IS  tons 

each.      How  many  such  cars  did  he  ship? 

12.  A  grocer  bought  a  quantity  of  butter  at  22  cents  a  pound, 

and  paid  for  it  all  $10.56.  How  many  pounds  did  he 
buy  ? 

13.  How  many  packages  containing  24  ounces  each  can  be 

made  from  15  pounds  of  tea? 

14.  A   man   sells   horses   at  $85   apiece.     How  many  horses 

must  he  sell  to  receive  $1,020? 

15.  How  many  loads  of  corn,  each  22  bushels,  will  be  needed 

to  fill  a  crib  that  holds  264  bushels? 


200 


THE   RATIONAL   ARITHMETIC. 


™''"* 

R^ 

m^mm 

'       ' 

mn 



■ 

'" 

"■" 

1.  This  is  the  plan  of  a  square  piece  of  ground  drawn  to  a 

scale  of  4-  an  inch  to  1  yard. 

2.  Measure  the  fi^rnre.     What  is  its  Icnifth?     Its  width? 

3.  How  many  feet  long  would  the  lot  be?     How  many  feet 

wide  ? 

4.  Count  the  number  of  square  yards.     By  wliat  name  have 

we  known  16i  feet?     By  what  name  have  we  known  5^ 
square  yards? 

5.  If  the  figure  were  B20  times  as  long  as  represented,  how 

long  would  it  be?     How  wide? 
G.   What  would  you  call  such  a  square  figure? 

7.  Referring  to  figure  A  on  page  152,  if  each  square  re])re- 

sents  1  square  inch,  how  long  would  the  side  of  this 
figure  be?    How  many  square  inches  would  it  contain? 

8.  How  many  square  inches  in  a  square  foot? 

9.  How  many  square  feet  in  a  square  yard? 
10.   How  many  square   yards  in  a  square  rod? 


PART   THIRD. 


201 


B 

A 

C 

D 

The  above  is  a  plan  of  a  g-aiden  drawn  to  a  scale  of  V2  feet  to  1  inch. 

1.  To  find  the  area  of  the  entire  garden,  first  divide  as  indi- 

cated by  the  (h)tted  lines. 

2.  The  area  of  B  is  ecpial  to  how  many  square  feet?     How 

many  square  yards? 

3.  Find  the  area  of   D  in  square  feet.       In   square  yards. 

The  area  of  C. 

4.  Find  the  area  of  A  in  square  feet.     In  square  yards. 

5.  Find  the  area  of  the  entire  garden  in  square  yards. 

6.  C  is  what  part  of  A? 

D  is  what  part  of  C  ?     Of  A  ? 

B  is  what  part  of  D  ?     Of  C  ?     Of  A  ? 

7.  If  1  inch  on  the  plan  represents  4  yards,  what  is  the  area 

of  each  section  in  square  yards?     In  square  feet? 

8.  If  1  inch  on  the  plan  represents  8  rods,  what  is  the  area 

of  each  section  in  square  rods? 


202  THE   RATIONAL   ARITHMETIC. 


Sq.  in. 

square  inch. 

Sq.  rd.  —  square  rod. 

Sq.  ft. 

—  square  feet. 

A.    -  acre. 

Sq.  yd. 

—  square  yard. 

Sq.  mi.        square  mile. 

1  sq.  ft. 

1  sq.  yd. 

1  sq.  rd.                  1  A.                   1  sq.  mi. 

14  I  sq.  in. 

I)  sq.  ft. 

^h  sq.  yds.           IGO  sq.  rds.      040  A. 

1.  In  GO  A.  liow  many  sq.  rd.  ? 

2.  In  32  sq.  rd.  ]iow  many  sq.  yd.  ? 

3.  In  63  sq.  yd.  how  many  s(]^.  ft.  ? 

4.  In  37  sq.  ft.  how  many  sq.  in.? 

5.  In  50  A.  and  13  sq.  rd.  how  many  sq.  rd.  ? 

().   In  47  sq.  rd.  and  1)  sq.  yd.  how  many  sq.  yd.? 

7.  In  37  sq.  yd.  and  7  sq.  ft.  how  many  sq.  ft.  ? 

8.  In  134  sq.  ft.  and  47  sq.  in.  how  many  sq.  in.  ? 

9.  Add: 

00  A.  15  sq.  rd.  IG  sq.  rd.  4  sq.  yd. 

137  A.  40  sq.  rd.  47  sq.  rd.  8  sq.  yd. 

250  A.  5G  sq.  rd.  G4  sq.  rd.  15  sq.  yd. 

18G  A.  49  sq.  rd.  32  sq.  rd.  3^  sq.  yd. 


10.  Add: 

14  sq.  yd.  2  sq.  ft.  4  sq.  ft.  43  sq.  in. 

11  sq.  yd.  4  sq.  ft.  G  sq.  ft.  84  sq.  in. 

4J  sq.  yd.  3  S(|.  ft.  7  sq.  ft.  17  sq.  in. 


11.  Subtract: 

18  sq.  ft.  5G  sq.  in.  IG  sq.  yd.  7  sq.  ft.  18  A.  8G  sq.  rd. 

5  sq.  ft.  13  sq.  in.  11  sq.  yd.  3  sq.  ft.  5  A.  17  sq.  rd. 

12.  Multiply: 

6  sq.  ft.  24  sq.  in.  6  sq.  yd.  3  sq.  ft.  3  A.  80  sq.  rd. 

G  3  2 


PART   THIRD.  203 

1.  A  board  is  13  feet  and  -4  inches  long  and  12  inches  wide. 

What  is  the  area  of  1  side  in  square  feet? 

2.  A  house  24  feet  wide  covers  72  square  yards  of  ground. 

HoAV  long  is  it  and  what  is  the  distance  around  it? 

3.  The  ])lackboards  in  a  schoolroom  are  equal  to  1  black- 

board 54  feet  long  and  4|  feet  wide.  How  many 
square  feet  of  surface  in  all  of  the  blackboards,  and 
what  will  it  cost  to  slate  them  at  86^/'  a  square  yard? 

4.  How  many  acres  of  ground  in  4000  square  rods? 

5.  What  will  a  farm  240  rods  long  and  (30  rods  wide  cost  at 

$35  an  acre? 

6.  A  man  has  10  acres  and  90  square  rods.     He  buys  8  acres 

and  70  square  rods.  How  much  land  does  he  then 
have  ? 

7.  How  many  square  feet  in  the  floor  of  a  room  that  is  24 

feet  long  and  124  feet  wide?  AVliat  Avill  it  cost  to 
paint  the  floor  at  25^/  a  square  yard? 

8.  How  many  square  yards  of  cloth  wall  it  take  to  cover  a 

tal)le  that  is  48  inches  long  and  36  inches  wide? 

9.  The  floor  of  a  hall   36  feet  long  and  6  feet  wide  is  paved 

with  marble  blocks  1  foot  square.  How  many  blocks 
did  it  take  to  pave  the  hall? 

10.  A  Jiall  24  feet  long  and  6  feet  wide  is  paved  with  tile  6 

inches  square.      How  many  tiles  were  required? 

11.  A  room   is   18   feet  long,  15  feet  wide  and  9  feet  high. 

How  many  square  yards  in  the  floor  and  ceiling.  How 
many  square  yards  in  the  walls? 

12.  How  many  square  feet  of  flooring  in  a  9  story  building 

which  is  55  feet  wide  and  123  feet  long? 

13.  How  many   square  feet  of  sidewalk  in  9  blocks  of  275 

feet  each,  if  the  sidewalk  is  8  feet  wide  ? 

14.  A  building  is   150  feet  long  and  40J  feet  wide.     How 

many  square  yards  does  it  .cover  ? 


204 


THE  RATIONAL  ARITHMETIC. 


13 

1 



2 

3 

4 

5 

6 

7 

13 
26 
39 
52 
65 
78 
91 


1.  18    X    2   = 

13    X    3    =:    _. 

13  X  4  r= 

2.  13  is  what  part  of  26? 

Of  91  ? 

3.  313  +  13  = 

2()  +  13  = 

52  +  13  := 

1.     8  0 


13  X  5  = 
13  X  6  = 
13  X  7  -: 


13 


1; 


D 


IL 
13 


Of  39?    Of  78?    Of  05?    Of  52? 

78  +  13  = 

()5  -f-  13  = 

91  -  13  = 

7  6  12  10  5 

13  13  13  13  13 


5.   How  many  stri[)es  in  our  flag? 
().   How  many  red  stripes? 

7.  How  many  white  ones? 

8.  When   was  the  number  of  stars  3  times   the  number  of 

stri[)es  ? 

9.  When  will  the  number  of  stars  be  1  times  the  number  of 

stripes  ? 

10.  5  times  the  number  of  stripes  in  our  flag  is  the  year  of 

the  nineteenth  century  in  which  the  Civil  War  closed. 
In  what  year  did  the  Avar  close? 

11.  From  the  Declaration  of  Independence   to  the  World's 

Fair  in  Chicago  Avas  9  times  as  many  years  as  there  are 
stripes  in  the  flag.     How  long  was  it? 


PART   THIRD.  205 

In  the  following  problems,  the  phrase  "  at  the  same  rate  "  or  its  equiv- 
alent is  understood  and  has  been  omitted  to  give  room  for  a  greater  number 
of  problems. 

.1.  3   pounds  of   butter    cost   75^.     What  is   the   cost  of  4 

pounds  ? 

2.  If  9  barrels  of  flour  cost  $45,  what  is  the  cost  of  7  bar- 

rels ? 

3.  5  acres  of  land  cost  $250.     What  is  the  cost  of  7  acres  of 

land  ? 

4.  I  received  $G3  for  9  weeks'  work.     What  should  I  receive 

for  12  weeks'  work? 

5.  What  is  the  cost  of  a  dozen  chairs  if  ^  of  a  dozen  cost 

$12? 

6.  If  I  pay  4^'  for  10  marbles,  what  should  I  pay  for  25 

marbles  ? 

7.  When  eggs  sell  at  80^-  for  2  dozen,  what  is  the  cost  of  i 

of  a  dozen? 

8.  A  dozen  pairs  of  boots  cost  $30.      What  is  the  cost  of  8 

such  pairs? 

9.  When  2  gallons  of  syrup  cost  $1.50,  what  is  the  cost  of  3 

quarts  ? 

10.  A  man  receives  $1200  a  year  and  spends  $45  a  month. 

How  much  does  he  save  the  first  0  months? 

11.  A  piece  of  string  is  0  lengths  of  an   18-incli  rule.     How 

many  feet  long  is  it? 

12.  A  man  had  on  his  wagon  30  bushels  of  wheat,  |  of  which 

he  sold  at  95^-  a  bushel.     The  remainder  he  sold  at  98^' 
a  bushel.      What  did  he  receive  for  the  entire  load? 

13.  The  curtains  for  a  room  with  3  windows  cost  $5.     What 

will  they  cost  for  a  room  with  12  windows? 

14.  3  dozen  neckties  cost  $1.80.      What  is  the  cost  of  4  neck- 

ties? 

15.  A  car  runs  4  miles  in  20  minutes.     How  far  will  it  run 

in  3  hours? 


206  THE   RATIONAL   ARITHMETIC. 

Note  —  In  plastering,  many  contractors  make  no  deductions  for  win- 
dows or  doors  on  account  of  the  extra  time  necessary  to  do  the  work  care- 
fully around  the  frames.  In  all  the  problems,  therefore,  on  plastering, 
unless  otherwise  stated,  the  walls  are  counted  as  solid. 

1.  A  room  is  9  feet  by  21  feet  and  9  feet  high.     How  many 

square  yards  in  the  walls?  In  the  ceiling?  What  will 
it  cost  to  plaster  the  walls  and  ceiling  at  21^  a  sq.  yd.  ? 

2.  A  room  is  12  feet  square  and  10  feet  high.     What  will 

it  cost  to  plaster  the  walls  and  ceiling  at  23^  per 
sq.  yd.  ? 

3.  What  will  be  the  cost  of  plastering  the  walls  of  a  room  9 

by  12  feet  and  9  feet  high  ac  45^'  a  square  yard? 

4.  What  will  be  the  cost  of  plastering  the  ceiling  of  a  room 

24  feet  square  at  28^'  a  square  yard? 

5.  Mr.  Jones  wishes  to  plaster  the  walls  and  ceilings  of  3 

rooms.  The  first  room  is  9  by  12  feet,  the  second  12 
by  15  feet  and  the  third  15  by  18  feet.  The  height  of 
each  room  is  9  feet.  What  will  be  the  cost  of  plaster- 
ing the  three  rooms  at  28^-  a  square  yard? 

6.  What  would  be   the   cost  of  carpet  a  yard  wide  for  the 

three  rooms  at  75^-  a  yard? 

7.  The  floor  of  a  room  contains  324  square  feet.      One  side 

of  it  is  4  yards  long.  How  many  yards  long  is  the 
other  side? 

8.  Tlie  4  walls  of  a  square  room   8   feet  high  contain   384 

square  feet.  What  is  the  length  and  the  width  of  the 
room  ? 

9.  The  top  of  a  desk  is  2  feet  and  6  inches  wide  and  4  feet 

long.      How  many  square  feet  does  it  contain? 

10.  What  is  the  length  of  a  wall  12  feet  high  the  area  of 

whose  side  is  3  times  2G4  square  feet? 

11.  A  room  is  10  feet  wide  and  11^  feet  long.     A  rug  on  the 

floor  is  2^  yards  wide  and  3  yards  long.  How  much  of 
the  floor  is  not  covered  by  the  rug? 


PART    THIRD. 

( 

u 

t 

14 

2 

28 

3 

42 

4 

56 

G 

70 

6 

84 

7 

98 

1.   AM: 
14 
14 

14               14                14 

14                28                56 
28                28                14 

14 

28 
56 

2.   14  X  3  == 
14  X  2  = 

14  X  5  - 

14  X  0  == 

14  X  7  =  - 

14    X    4    rr    _ 

207 


28 
28 
42 

14)98 

14)70 


3.  14  is  what  part  of  28  ? 

4.  How  many  28's  in  42? 

5.  42  is  how  many  14's? 

6.  56  is  how  many  14's? 

98? 

7.  70  is  how  many  14's? 

of  98? 

8.  84  is  how  many  14's? 


Of  56?     42?     70?     84? 
70?     84?     56?     98? 
28's?     What  part  of  56?     Of  70? 
28's?     42's?     What  part  of  70? 

28's?     42's?     56's?     What  part 

28's?     42's?     56's?     70's? 


9.   A  man   fed  his  horse   1t\  pecks  of  oats  each   day   for  4 
weeks.     How  many  bushels  of  oats  did  he  feed  him  ? 

10.  Mr.  Jones  traveled  195  mi.  each  day  for  2  weeks.     How 

far  did  he  travel  in  the  two  weeks? 

11.  A  train  ran   14  miles  in   30  minutes.      How  far  would  it 

run  at  this  same  rate  in  2-J  hours  ? 

M 

12.  A  piece  of  ground   1008  ft.  wide  is  divided  into  14  equal 

lots.     What  is  the  width  of  each  lot? 


J08 


THE   RATIONAL   ARITHMETIC 


PART   THIRD.  209 

1.  Review  page  121. 

2.  How  long  is  the  base  of  the  triangle  A  on  the  opposite 

page  ? 

3.  What  is  the  altitude  of  the  triangle? 

4.  Into  what  rectangle  can  you  change  the  triangle  AV 

5.  What  is  the  area  of  this  rectangle? 

6.  What,  then,  is  the  area  of  the  triangle  A? 

7.  What  rule  would  you  give  for  finding  the  area  of  such  a 

triangle  ? 

8.  Measure  the  triangles  B,  C,  D  and  E,  and  give  tlie  dimeu- 

sions  in  each  case  of  the  rectangle  into  which  you  can 
change  the  triangle. 

9.  What  is  the  area  of  each  of  these  rectangles? 

10.  What,  then,  is   the  area  of  the  triangle  B?     Of  the  tri- 

angle C  ?       Of  E  ? 

11.  If  you  were  to  make  a  rectangle  Avliose  widtJi  was  the  base 

of  A,  and   whose   length   was   the   altitude  of  A,  would 
you  change  the  largest  angle  of  the  triangle? 

12.  Such    an   angle  we  call   a  right  angle  and  every  triangle 

which  has  such  an  angle  is  called  a  right-angled  tri- 
angle. 

13.  What   triangles   on   the   opposite   page   are    right-angled 

triangles  ? 
11.   If  an  inch  of  the  plan  represented  a  yard,  what  would  l>e 

the  area  of  each  triangle  in  feet? 
15.   Find  the  area  of  the  following  right-angled  triangles: 

Base  three  feet,  altitude  six  feet. 

Base  four  feet,  altitude  three  feet. 

Base  six  feet,  altitude  eight  feet. 

Base  eight  feet,  altitude  ten  feet. 

Base  tAvelve  feet,  altitude  eight  feet. 

Base  fifteen  feet,  altitude  twelve  feet. 

Base  ten  inches,  altitude  five  inches. 


210 


THE   RATIONAL   ARITHMETIC, 


PART   THIRD.  211 

Note.— The  plan  on  the  opposite  page  represents  a  garden,  which  has 
been  cut  into  various  parts  by  the  walks  running  through  it.  The  plan  is 
drawn  to  the  scale  of  10  feet  to  an  inch. 

1.  Measure  the   line   around   the   entire   plan   and  find   the 

length  of  the  path  around  the  gai'den. 

2.  From  these  measurements,  what  is  the  area  of  A? 

3.  What  is  the  area  of  B? 

4.  What  is  the  area  of  C? 

5.  Wliat  is  the  area  of  I)? 
(>.   What  is  the  area  of  E? 

7.  Wiiat  is  the  area  of  F? 

8.  How  many  square  feet  are  there  in  the  entire  garden? 

9.  A  is  what  part  of  B?     C?     D?     E?     F? 

10.  F  is  what  part  of  the  entire  garden  ? 

11.  How  did  you  find  the  area  of  C? 

12.  How  did  you  find  the  area  of  D? 

13.  In  what  other  ways  beside  finding  the  areas  of  tlie  tri- 

angles could  you  find  the  area  of  tlie  entire  garden  ? 

NoTK. — Suppose  the  plan  on  the  opposite  page,  representing  a  piece  of 
land,  is  drawn  to  a  scale  of  one  inch  to  8  rods. 

14.  What  will  be  the  value  of  A  at  25^^-  a  sq.  vd.  ? 

15.  What  will  be  the  value  of  B  at  30^/  a  sq.  rd.  ? 
1().  What  will  be  the  value  of  C  at  28^'  a  sq.  rd.  ? 
IT.  What  will  be  the  value  of  D  at  27^/  a  sq.  rd.  ? 

18.  What  will  be  tlie  value  of  E  at  21^-  a  sq.  id.  ? 

19.  What  w^ill  be  the  value  of  F  nt  29^-  a  sq.  yd.  ? 

20.  How  many  sq.  rds.  in  the  entire  field? 

21.  How  many  acres? 

22.  How  many  sq.  yds.  in  A? 

23.  How  many  sq.  ft.  in  B? 

24.  How  many  sq.  yds.  in  C? 

25.  How  many  sq.  ft.  in  1)? 
2*).  How  many  sq.  yds.  in  E? 
27.  How  many  sq.  ft.  in  F? 


212  THE   RATIONAL   Altl  ITIMETIU. 

1.  A  woman  who  raises  cliickens  puts  13  eggs  under  each  of 

6  hens.  The  first  hatched  out  all  but  1,  the  second  all 
but  2,  tlie  third  all  but  3,  tlio  fourth  all  but  4,  and  the 
others  aJl  but  5  eacli.  How  many  chickens  were 
liatched  ? 

2.  How  many  pigeons  will  it  take  to  pick  up  a  bushel  of  corn 

(5G  lbs.)  if  each  one  picks  up  1  oz.  ? 

3.  A  man  buys  12  tons  of  hay  for  $80  and  sells  it  for  60'/- 

per  cwt.      How  much  does  he  make? 

4.  An  expressman  receives  $3.25  per  day  for  30  days.     It 

costs  him  30^'  per  day  to  feed  his  horse.  He  pays  $4.20 
for  repairs  to  his  wagon.      How  much  has  he  left? 

5.  An  express  company   carries  400  packages  at  15^/  each, 

28  trunks  at  50^/  each,  and  12  bicycles  at  40^'  each. 
What  does  it  get  for  them  all  ? 

6.  There  are  40  street  cars  on  one  line  and  each  can  carry 

00  people.  How  many  people  will  they  all  carry  in  12 
round  trips  if  I  carry  their  full  number  each  way  and 
the  remainder  carry  30  persons  each  way? 

7.  A  baker  has  400  loaves  of  bread.      He  sells  f  at  5y^  per 

loaf,  60  loaves  at  4r(/-,  and  gives  the  rest  away.  How 
much  does  he  get  for  the  bread  ? 

8.  How  many  sheej)  luust  there  be  to  produce  a  ton  of  wool 

if  the  wool   from   each   sheep  weighs  4    11  )S.?      If  each 
sheep  produces  5  lbs.  ? 
1).    How  many  balls   of  kite   string  will  it  take  to  reach  1| 
miles  if  each  ball  contains  200  yards?     300  yds.? 

10.  A  farmer  raised  840  bu.  of  potatoes  on   5  acres  of  land. 

Wliat  was  the  value  of  the  average  produce  of  1  acre  at 
40^'  per  bushel? 

11.  A  man  set  out  12,000  cabbag(^  plants,  but   J   of  them  died 

and  -jQ  of  the  remainder  were  stolen.  What  did  he  re- 
ceive for  the  rest  at  $3  per  hundred? 


PART   THIRD.  213 

1.  An  orchard  of  600  trees  produced  3  bbls.  of  apples  to  the 

tree.  The  owner  sold  them  at  $1.  40  per  bbl.,  but  the 
barrels  cost  him  25^  each.  What  did  he  get  for  the 
apples  after  paying  for  the  barrels  ? 

2.  A  peach  orchard  produced  210  ])u.  of  peaches.      If  1  bu. 

fills  5  baskets,  what  is  the  value  of  the  crop  at  20^'  a 
basket  ? 

3.  A  farmer  pays  some  boys  1</  per  box  for  picking  berries, 

and  the  boxes  cost  him  \(l'  each.  If  he  sells  1000  boxes 
of  berries  for  $60.00,  what  is  his  share  of  the  money? 
L  A  boy's  pay  for  a  week's  work  at  berry-picking  at  1^/  per 
box  Avas  -$5.40.  How  many  boxes  did  he  pick  daily,  on 
an  average,  during  the  six  days? 

5.  A  farmer  sells   1000  boxes  of  berries  to  a  city  grocer  at 

6^  per  box.  It  costs  the  grocer  $5.00  to  get  them  to 
the  city  and  he  sells  them  at  8</  per  box.  What  is  his 
gain? 

6.  A  woman  who  kept  chickens  bought  12  bu.   of  feed  for 

them  at  35^/  per  bu.  She  sold  120  doz.  eggs  at  12J^- 
a  doz.  and  40  chickens  at  25^/*  each.  What  was  her 
gain  ? 

7.  How  many  chickens  averaging  5  lbs.  each  and  worth  6^ 

per  lb.  can  be  bought  for  $75  ? 

8.  If  15  chickens  are  worth  fis  much  as  1  sheep,  and  6  sheep 

are  worth  as  much  as  1  cow  costing  $28.80,  what  is  1 
chicken  worth? 

9.  A  carpenter  builds   a   fence   for  $56.     The  lumber  costs 

him  $15  and  he  pays  each  of  three  men  $2.75  per  day 
for  four  days.  What  is  his  share  of  the  $56? 
10.  A  man  earns  $1.50  every  day  he  works  and  pays  50^  a  day 
for  his  board.  If  he  oidy  works  16  days  during  the 
month  of  May,  how  much  has  he  left  after  paying  his 
board? 


214 


THE   RATIONAL  ARITHMETIC. 


J.   Review  pages  69  and  128. 

2.  How  many  edges  do  you  see 
on  this  block?  How 
Tuaiiy  edges  has  this 
l)lock? 

3.  Measure  its  edges.  How 
long  aio  they?  Are  all 
the  edges  of  the  block  of 
equal  length?  What  do 
you  call  sucli  u.  block? 

4.  If  you  sliould  place  12  of  these  (*a])es  in  a  r(3W,  how  long 

wouUl  the  row  be? 

5.  If  you  should   {)]ace    12  of  tJiose  rows  side  by  side,  how 

wide  wouhl  tlie  whole  be? 
B.   How  many  cubes  would  y(^u  use? 

7.  What  figure;  would  the  upper  surface  of  the  cubes  form? 

8.  How  ma!iy  s(]uare  inches  would  there  be  in  this  surface? 

How  many  inch  cubes  would  you  use  in  forming  this 
layer  ? 

9.  If   you   sliould    ])lace    another    layer    of   cubes   on    those 

already  used,  how  many  cu])ic  inches  would  you  have? 
How  many  if  you  used  3  layers?  4  layers?  5  layers? 
6  layers?     7  layers?     8?     9?     10?      11?     12? 

10.  Su[)pose  the  picture  represents  12  layers  of  inch  cubes, 

each  layer  containing  12  rows 'of  12  cubes  each.  What 
would  the  edges  measure?  What  would  you  call  such 
a  cube?     How  many  cubic  inches  would  it  contain? 

11.  If  you  should  take  one-half  of  this  cube  and  divide  into  4 

equal  cubes,  what  would  each  cube  measure? 

12.  What  part  of  the  whole  cube  would  each  be? 

13.  How  many  cubic  inches  in  each  part? 

14.  How  many  cubic  inches  in  three-eighths  of  a  cubic  foot? 

In  seven -eighths?     In  one-fourth?     In  three-fourths? 


PART   THIRD.  215 

1.  A  strawberry  box  is  6  iiiclies  long,  4  inches  wide  and  4 

inches  deep.     How  many  sucli  boxes  can  be  packed  in 
a  case  2  feet  long,  1  foot  wide  and  |  of  a  foot  high? 

2.  There   are   231   cubic   inches   in    1   gallon.      How   many 

gallons  can  be  put  into  a  pail  holding  693  cubic  inches? 

3.  How  many  boxes  12   iiiclies   ](jng,  0  inches  wide   and  3 

inches  high  can  b(;  [>M,ck(Ml  in  a  case  6  feet  long,  4  feet 
wide  and  4  feet  high  ? 

4.  How  many  cubic  feet  of  ;iir  will  a  glass  jar  24  inches  long, 

18  inches  wide  and  12  iuclx's  liiijli  hold? 

5.  From   a  vessel   liolding   2  cubic  feet  of  water  864  cubic 

inches  were  tfdvon.      How  many  cubic  inches  remain? 
How  many  (;ubic  feet? 

6.  In  1  jar  there  are   81)4  cubic  inches  of  liquid;  in  another 

2592  cubic  indies.      How  many  cubic  feet  in  a  third 
jar,  holding  as  much  as  the  first  and  second  together? 

7.  A  ]nan  put  12  inches  of  sand  into  a  box  9  feet  long  and 

5    feet   wide.       How  many  cubic  feet   of   sand   in    the 
box  ? 

8.  A  wagon  box  3  feet  Avide  and  9  feet  long  is  1^  feet  deep. 

How  many  cubic  feet  will  it  hold? 

9.  A  ditch  45  feet  long  and  2  feet  wide  contains  (530  culnc 

feet.     How  deep  is  the  ditch? 

10.  A  freight  car  is  32  feet  long  and  ()  feet  wide  inside  and  is 

filled  with  sand  3£  feet  deep.      How  many  cubic  feet  of 
sand  are  in  the  car? 

11.  A  wall  is  44  feet  long  5^  feet  high  and  18  inches  thick. 

How  many  cubic  feet  in  the  wall? 

12.  A  sidewalk  is  6  inches  thick  and  6  feet  wide.     How  many 

cubic  feet  in  124  feet  of  the  sidewalk? 

13.  In  a  building  there   are   18   pillars  2  feet  by  18  inches 

and    14   feet    high.       How   many   cubic   feet   in   these 
pillars  ? 


216 


THE   RATIONAL   ARITHMETIC. 


Cu.  in.  =  cubic  inch 
1  cu.  ft.             1  cu.  yd. 

1728  cu.  in.        27  cu.  ft. 

1.  Add: 

cu.  ft.   : 

1  cord 
128  cu. 

-  cubic  foot 
Igal. 
ft.       2.31  cu.  in. 

cu.  yd.  = 
Ibu. 
21501  cu. : 

cubic  yard 
in.  (nearly) 

cu.  yds. 

7 

cu.  ft. 

6 

cu.  in. 

27 

cu.  yds. 

6 

cu.  ft. 

14 

cu.  in. 

55 

2 

10 

250 

2 

2 

17 

4 

2 

41 

3 

3 

40 

8 

3 

3 

1 

2 

160 

8 

4 

120 

8 

4 

50 

cu.  yds. 

20 

cu.  ft. 

10 

cu.  in. 

75 

cu.  yds. 

4 

cu.  ft. 

7 

cu.  in. 

800 

7 

5   ' 

50 

7 

6 

600 

5 

1 

64 

3 

4 

20 

3 

8 

125 

2 

2 

8 

2 

3 

800 

9 

7 

300 

2.  Subtract: 

cu.  yds. 
10 

cu.  ft. 

25 

cu.  in. 

1200 

cu.  yds. 
9 

cu.  ft. 

18 

cu.  in. 

350 

6 

16 

900 

• 

5 

9 

275 

cu.  yds. 

14 

cu.  ft. 

20 

cu. in. 

800 

cu.  yds. 
11 

cu.  ft. 

15 

cu.  in. 

920 

7 

13 

246 

6 

cu.  yds. 
12 

7 

cu.  ft. 

6 

256 

3.  Multiply: 
cu.  yds.        cu.  ft. 

6              7 

cu.  in. 

576 

cu. in. 

432 

3 

4 

cu.  yds. 

4 

cu.  ft. 

13 

cu. in. 

864 

cu.  yds. 

4 

cu.  ft. 

2 

cu.  in. 

192 

2 

9 

PART   THIRD.  21? 

1.  A  boy  carried  enough  wood  to  make  a  pile  4  ft.  long,  2  ft. 

wide  and  2  ft.  high.     What  part  of  a  cord  did  he  carry? 

2.  What  must  be  the  cubic  contents  of  a  jar  to  hold  f  of  a 

gallon  ?     2i  gals.  ?     44  gals.  ? 

3.  How  many  cubic  inches  are  there  in  a  bin  holding  2  bu.  ? 

^  bu.  ?     ^  bu.  ?     4|  bu.  V     6i  bu.  ? 

4.  A  cord  of  wood  is  usually  piled  8  ft.  long  and  4  ft.  wide. 

How  high  is  it? 

5.  A  bin  holds  16  bu.     How  many  cubic  inches  does  it  con- 

tain? 

6.  A  water  trough  contains  12  gals,  of-  water.     It  is  14  in. 

wide  and  9  in.  deep.     How  long  is  it? 

7.  How  many  cu.  yds.  of  earth  will  be  excavated  for  a  cellar 

that  is  24  ft.  long,  21  ft.  wide  and  12  ft.  high? 

8.  From  a  cellar  36  ft.   long  and  18  ft.  wide  6804  cu.  ft.  of 

earth  was  taken.      How  deep  was  the  cellar? 

9.  How  many  cu.  yds.  of  rock  was  blasted  from  a  tunnel  that 

is  9 J  ft.  high,  80  ft.  long  and  12|  ft.  wide? 

10.  A  cubic  foot  of  water  weighs  1000  ounces.      What  will 

water  enough  to  fill  a  trough  6  ft.  long,  2  ft.  wide,  and 
li  ft.  deep  weigh  in  pounds  ? 

11.  If  oil  weighs  -J  as  much  as  water,  what  is  the  weight  of  a 

cubic  foot  of  oil  in  pounds? 

12.  A  street  sprinkler  holds  168  cu.  ft.  of  water.      How  much 

does  it  hold  in  pounds  ? 

13.  If  such  a  street  sprinkler  is  emptied  every  24  minutes 

during  9  hours,  how  many  buckets  of  water  are  used  if 
a  bucket  holds  ^  of  a  cu.  ft.  ? 

14.  A  rectangular  tank  6  ft.  wide,  10  ft.  long,  and  3  ft.  deep 

is  full  of  water.      What  is  the  weight  of  the  water? 

15.  35  cu.  ft.  of  coal  will  weigh  about  2000  pounds.     How 

many  tons  will  a  wagon  box  7  ft.  long,  5  ft.  wide,  and 
J  ft.  high  weigh  if  loaded  full  ? 


218 


THE    RATIONAL   ARITHMETIC. 


/ 

[5 

1 

2 

3 

4 

5 

6 

15 
30 
45 
60 
75 
90 


1.  Add 
15 
15 
15 


2.  15  X  2  = 
15  X  4  = 
15  X  5  = 


15 
30 
15 


15 
45 
15 


15 

fiO 
15 


15 
80 
45 


15  X  3 
15  X  () 
15)45 


30 
30 
30 

15)G0 

15)90 


3.  15  is  what  part  of  30?     60?     45?     90?     75? 

30  is  how  many  15's  ?     What  pai-t  of  45  ?     00  ?     75  ?     90  ? 
45  is  how  many  15's?     How  many  30's?     What  part  of 

00?     Of  75?     90? 
OOis  how  many  15's?     How   many   30^s?      45's?     AVJiat 

part  of  75?  '  Of  90? 
75  is  how  many   15's?     How  many  30's?     45'sf     OO's? 

What  part  of  90? 
OOis  how  many   15's?     How  many  30's?     45's?     OO's? 

75's? 

4.  A  boy  bought  3  dozen  oranges  at  the  rate  of  15^/  a  (hizen. 

AVliat  did  they  cost  him  ? 

5.  A  girl  bought  12  liandkerchiefs  at  the  rate  of  2  for  15r/. 

WJiat  did  they  cost  her? 

6.  Railroad  fare  for  a  picnic  excursion  was  15^  for  the  round 

trip.     How  much  was  collected  on  a  train  of  9  cars 
with  65  persons  in  each  car? 


PART   THIRD.  219 

1.  At  a  school  entertainment  there  were  186  grown  people 
who  paid  15^/  eacli  and  824  children  at  lOf/-  each.  The 
expenses  were  $15.25.  How  much  was  left  for  the 
school  ? 

3.  A  class  of  25  pupils  have  a  spelling  lesson  of  15  words. 
15  of  them  write  the  lesson  once,  6  of  them  write  it 
twice,  and  4  write  it  three  times.  How  many  words  do 
they  all  write  ? 

3.  The  pupils  of  a  school  put  $14.06  into  the  Penny  Savings 

Bank  on  Monday  and  take  out  $2.40;  they  put  in  $7.24 
on  Wednesday  and  take  out  $1.56,  and  they  put  in 
$1).28  and  take  out  $4.10  on  Friday.  How  iiiuch  more 
do  they  put  in  than  they  take  out  for  the  week? 

4.  A  peddler  buys    15   bu.   of  nppkis  at  90^/  per  busJjel  and 

sells  them  at  15^/  ])er  half  peck.  How  much  does  he 
make  if  he  sells  them  all? 

5.  A  banana  ])eddler  buys  100  dozen  bananas  for  $7.50.     He 

sells  ^  of  them  nt  15<'/  per  dozen,  4  of  them  at  KK/  per 
dozen,  20  dozen  at  5'/  ])er  dozen,  and  the  rest  spoiled. 
How  much  does  he  make? 

6.  A  junk  dealer  buys  1000  pounds  of  old  iron  for  $1.20  and 

400  pounds  of  lead  for  $6.  He  sells  the  iron  for  ^^/'  per 
pound  and  the  lead  for  3|^-  per  pound.  How  much  does 
he  make? 

7.  A  milk  dealer  sells  every  day  6  cans  of  milk  each  holding 

8  gallons.  How  many  customers  has  he  if  each  one 
takes  2  qts.  ?     If  each  takes  3  pts.  ? 

8.  If  he  pays  90^-  per  can  for  the  milk,  and  sells  it  for  5^* 

per  quart,  how  much  does  he  gain  ? 

9.  A  sugar  plantation  in  Cuba  produces   480  lilids.  of  sugar, 

averaging  540  lbs.  in  weight.  What  is  the  value  of 
the  sugar  at  2|-^'  a  pound?  At  2^'  a  pound,  what  is  the 
value  of  the  sugar  from  15  such  plantations? 


220  THE    RATIONAL   ARITHMETIC. 


gi.  =  gill, 
pt.  =  pint. 

qt.  =  quart, 
gal.  =  gallon. 

bbl.  = 
hhd.  = 

barrel. 
=  hogshead. 

1  pt.                  1  qt. 
A  gi.                  2  pts. 

1  gal.               1  bbl. 
4  qts.                31^gais. 

(commonly) 

1  hhd. 

2  bbls. 

1.  Review  pages  74 

and  130. 

2.  Add: 

gals.    qts.     pts. 

4       2       1 

gals,    qts.    pts. 

7       3 

bbls. 

2 

gals.      qts. 

14       1 

3       11 

2               2 

3 

6       3 

bbls.   gals.     qts. 

1       20       1 

• 

gals.     qts.     pts. 
15                1 

hhcl 
1 

.  bbls. 

gals.     qts. 

16       1 

11       1 

2       3 

1 

15       1 

3.  Subtract: 

gals.   qts.     pts. 
7       4         2 

gals.    qts.    pts. 

4       2       2 

gals. 
14 

qts.     pts. 

6       3 

3       3         1 

2       11 

4 

4       2 

bbls.    gals.     qts. 

3       30       2 

bbls.     gals.     qts. 

4       15       3 

hhcl, 

2 

,  bbls. 
1 

gals.     (|ls. 

31       2 

1       21 

2                 1 

1 

8       1 

1.  Multiply: 

gals.    qts.     pts. 

2       3       1 

gale.    qts.     pts. 

7       12 

« 

bbls. 

2 

gals.     <(ts. 

10       2 

2 

4 

3 

5.  A  milkman  starts  witli  42  gals. ;  sells  -|  of  the  milk  to  pri- 

vate customers,  the  rest  to  a  hotel.     How  many  quarts 
does  he  sell  to  the  hotel? 

6.  A  druggist  put  1  qt.  of  liquid  into  bottles  holding  |  gi. 

each.     How  many  bottles  did  he  use? 

7.  How  many  jelly  glasses  holding  |   of  a  pt.   each  can  be 

filled  from  1  gal.  of  jelly  ? 


PAirr    THIRD.  2'Zl 

1.  How  many  pint  bottles  will  hold  2  gals.  1  pt.  of  vinegar? 

What  is  it  worth  at  13^*  a  quart? 

2.  If  a  gallon  of  wine  cost  $4,  what  will  5  pts.  cost? 

3.  From  a  milk  can  holding  8  gals.,  ^^g  of  the  milk  was  spilled. 

How  many  quarts  were  left?     How  many  gallons? 

4.  How  much  ice  cream  will  a  man  make  if  he  uses  a  gallon 

and  a  half  freezer  and  has  it  full  twice,  and  half  full 
the  third  time? 

5.  How  many  gals,  in  412  gills? 

().  What  part  of  12  gals,  is  4|  gals.  ? 

7.  A  man  sold  12  cans  of  mineral  water,  each  holding  6  gals. 

at  15^  per  gal.     How  much  did  he  receive? 

8.  How  many  oil  barrels,  each  holding  45  gals.,  can  be  filled 

from  a  tank  holding  10,800  gals,  of  oil? 

9.  A  hotel  uses  25  gals.  3  pts.  of  milk  each  day.      How  much 

does  it  use  in  3  w^eeks? 

10.  There  are  231  cu.  in.  in  1  gal.     How  many  cubic  inches 

in  a  bottle  holding  2  qts.  ? 

11.  How  many  cubic  inches  in  a  cistern  holding   10  bbls.  ? 

12  bbls.  ?     16  bbls.  ? 

12.  En  a  jar  that  holds  2  gals.,  3  qts.  of  water  are  placed. 

How  many  cubic  inches  of  the  jar  are  unfilled? 

13.  From  a  barrel  of  vinegar  a  grocer  fills  2  four-gallon  jugs 

and  puts  3  gals,  and  1  qt.  in  another  jug.  How  many 
gals,  had  he  left? 

14.  A   man  sells   3  gals,  and  2  qts.   of  molasses  to  one  cus- 

tomer; 2  gals,  and  1  qt.  to  another  customer,  and  1  qt. 
and  1  pt.  to  a  third.  How  many  quarts  did  he  sell  in 
all?     How  many  gallons? 

15.  From  a  barrel  full  of  rain  water,  80  qts.  were  taken  out  at 

different  times.  The  water  remaining  in  the  barrel 
measured  40  qts.,  the  rest  having  evaporated.  How 
many  quarts  had  evaporated? 


'•JO'-) 


THE   RATIONAL   ARITHMETIC. 


Add 

16 
16 


16 

1 

■  ■ 

2 

3 

4 

5 

6 

16 
32 


16 
16 

32 


16 

32 

32 


16 
32 
48 
64 
80 
06 


16 
32 

48 


48 

48 


2.  16  X  3  :=  _.  16  X  5  = 

16  X  2  == 16  X  6  =: 

16  X  4  = 

3.  16  is  what  part  of  32?     48?     64?     80?     96? 

4.  32  is  how  many  16's?     What  part  of  48?     Of  64?     80? 

96? 

5.  48  is  how  many  16's?     How  many  32's?     Wlmt  part  of 

64?     Of  80?     96? 

6.  64  is  how  many   16's?     How  many  32's?     48'sV     What 

part  of  80?     Of  96?  ' 

7.  80  is  how  many  16's?     How  many  32"s?     48's?     64's? 

What  part  of  96  ? 

8.  96  is  how  many   16's?     How  many   32's?     48's?      64's? 

9.  A  farm  of  96  acres  was  divided  into  16  equal  parts.      How 

many  acres  in  eacii? 

10.  In  a  square  mile  of  land  there  are  16  farms  equal  in  size. 

How  many  acres  in  each?  If  one  of  these  farms  is  di- 
vided into  3  fields,  two  of  which  contain  K)  acres  each, 
what  is  the  area  of  the  third  field? 

11.  From  a  bin  containing  80  lbs.  of  meal,  2  eight-lb.  pack- 

ages were  taken.  How  many  sixteen-lb.  packages  can 
be  made  from  the  remainder? 


PART   THIRD.  223 

1.  A  brick  mason  contracts  to  build  a  chimney  for  $72.     If 

it  takes  10  clays  to  do  the  work  and  he  pays  each  of  his 
2  helpers  $1.50  per  day,  what  is  his  rate  of  pay  per 
day? 

2.  A  man  agreed  to  haul  away  1560  cu.  yds.  of  clay  for  $264. 

He  paid  4  teamsters  $3.90  each  per  day  for  13  days. 
How  much  did  he  have  left  ?  What  did  each  teamster 
receive  ? 

3.  If  each  teamster  was  paid  at   the  rate  of  13^*  per  cu.  yd., 

how  many  yds.  did  he  haul  to  earn  what  he  received? 

4.  A  man  hauls  sand  for  \)(J-  per  cu.  yd.     If  his  wagon  holds 

1|-  cu.  yds.  and  he  hauls  18  loads  per  day,  what  is 
his  daily  pay? 

5.  A  newsboy  buys  his  papers  at  the  rate  of  10  for  6^'  and 

sells  them  for  1^'  each.  How  much  will  he  gain  if  he 
sells  75  papers?     120  papers? 

6.  He  sells  45  on  Monday,  54  on  Tuesday,  81  on  AVednes- 

day,  and  70  on  Thursday.  AVliat  does  he  gain  in  the  4 
days  ? 

7.  On  Friday  he  buys  100  papers  and  sells  all  but  5  that 

are  spoiled  by  the  rain.  What  does  he  receive  for  his 
work  on  Friday? 

8.  A  newspaper  prints  1|   million  copies  in  6  days.     At  the 

end  of  the  week  13,526  copies  had  been  given  away 
and  29,674  copies  were  left  on  hand.  What  was  the 
average  daily  circulation? 

9.  If  \  of  these   papers  are  sold   by  newsboys,  how   many 

newsboys  must  there  be,  if  each  one  sells  100  papers 
every  day? 
10.  A  man  divides  80  acres  of  land  into  streets  and  building 
lots.  The  streets  take  up  ^g  of  the  land,  and  the 
remainder  is  divided  into  blocks  each  containing  3  A. 
How  many  blocks? 


224  THE   RATIONAL   ARITHMETIC. 

1  qt.  =  2  pt.  pk.  =  peck.  bu.  =  bushel. 

1  pk.  =  8  qt.  1  bu.  :=  4  pk. 

1.  Review  pages  76  and  131. 

2.  Add: 

3  bu.,  1  pk.,  6  qt.      1  bu.,  2  pk.,  3  qt.      2  bu.,  3  pk.,  4  qt. 
1  bu.,  2  pk.,  1  qt.       2  bu.,  1  pk.,  5  qt.     3  bu.,  4  qt. 

4  bu.,  2  pk.,  5  qt.       5  bu.,  2  qt.     3  bu.,  3  pk.,  7  qt. 
1  bu.,  2  pk.,                            3  pk.,  6  qt.  1  qt. 

3.  Subtract : 

5  bu.,  3  pk.,  6  qt.       3  bu.,  2  pk.,  7  qt.      6  bu.,  1  pk.,  5  qt. 

1  bu.,  2  pk.,  4  qt.       2  bu.,  5  qt.      1  bu.,  1  pk.,  1  qt. 

4  bu.,  2  pk.,  4  qt.      8  bu.,  3  pk.,  5  qt.     12  bu.,  2  pk.,  6  qt. 
1  pk.,  4  qt.       2  bu.,  2  pk.,  2  qt.        7  bu.,  4  qt. 

4.  Multiply. 

2  bu.,  2  pk.,  3  qt.      3  bu.,  1  pk.,  3  qt.     4  bu.,  1  pk.,  1  qt. 
2__      3_  4 

5.  How  many  bushels  in  128  pks.  ?     In  150  pks.  ? 

(3.  How  many  quart  boxes  will  1  bu.  3  pks.  2  qts.  fill  ? 

7.  Find  cost  of  3  pks.,  6  qts.,  1  pt.  of  nuts,  at  12i^  a  pint? 

8.  In  96  qts.  how  many  pecks?     How  many  bushels? 

9.  What  part  of  7  bu.  are  7  pks.  ?     7  qts.  ? 

10.  How  many  quarts  of  cherries  can  be  bought  for  $2,  if  1 

bushel  of  cherries  is  worth  $3.20? 

11.  I  bought  7  bu.  3  pks.  of  potatoes  on  Monday;  8  bu.  on 

Tuesday  and  10  bu.  1  pk.  6  qts.  on  Wednesday.     How 
many  potatoes  did  I  buy  in  all? 

12.  A  teamster  feeds  his  horses  36  qts.  of  oats  a  day.     How 

long  will  120  bu.  of  oats  last  him?     What  does  it  cost 
him  each  day  when  oats  are  worth  27^  a  bu.  ? 


PART   THIRD.  225 

1.  From  a  sack  of  peanuts  holding  3  bu.,  25  qts.  were  taken. 

How  many  bushels  remained? 

2.  A  bushel  of  plums  is  divided  equally  among  12  people. 

How  many  quarts  did  each  receive? 

3.  How  many  pecks  of  beans  will  a  man  sell  who  sells  3  qts. 

to  each  of  8  customers? 

4.  A  woman  measuring  out  2J  qts.  of  flour  uses  a  measure 

holding  J  pt.  How  many  times  does  she  fill  the  meas- 
ure? 

5.  A  barrel  of  apples  was  sold  in  3  lots.      The  first  sale  was 

1  bu.  and  2  pks. ;  the  second  2  pecks;  the  third  IJ 
bu.     How  many  bushels  were  there  in  the  barrel? 

6.  From  3  bushels  of  peas,  a  man  sells  ^  peck  to  one  cus- 

tomer; 4  qts.  to  another,  1  pk  to  another.  How  many 
has  he  left? 

7.  If  one-half  a  peck  of  peaches  when  canned  make  3  qts., 

how  many  bushels  must  be  bought  to  make  36  qts.  of 
canned  peaches? 

8.  A  man  bought  at  a  feed  store  5  bu.  of  corn,  2  bu.  and  3 

pks.  of  oats  and  IJ  bu.  of  mixed  feed.  He  had  at  home 
in  the  bins,  3  pks.  of  corn,  ^  bu.  of  oats  and  1  pk.  of 
ground  feed.  How  many  bushels  of  feed  did  he  have 
in  the  bins  after  he  received  what  he  bought? 

9.  In  one  year  a  farmer's  family  used   50^  bu.  of  potatoes. 

He  saved  9  bu.  3  pks.  for  planting  and  sold  117  bu. 
and  S^  pks.     How  many  busliels  did  he  raise  that  year  ? 

10.  240  boxes  of  peaches,  holding  1  pk.  each,  were  shipped  to 

market.  The  fruit  was  picked  in  one-half  bu.  baskets. 
How  many  baskets  of  fruit  were  there? 

11.  A  fruit  dealer  bought  2  crates  of  strawberries,  each  hold- 

ing 24  qts. ;  and  6  crates,  each  holding  32  qts.  The 
berries  were  put  into  pint  boxes  and  sold  for  10^  a 
box.     What  did  the  dealer  receive  for  the  berries  ? 


226 


THE   RATIONAL  ARITHMETIC. 


1 

6% 

1 

2 

3 

4 

5 

6 

1.   Add: 
16 1 
16f 


16^ 


J.Ug 

50 


331 
33i 


333^ 

50 

833^3 
lOO 


16| 


83| 
16| 


2.  16|  X  3  = 
16|  X  2  = 
16|  X  4  := 


161  X  6 


16-1 


X  6  = 


66|? 
66f? 


331? 

831? 


831? 


33i's? 


33i's? 
331 's? 
33i's? 


100? 
What    part    of    ()6|? 

50's? 

50^s?     66|'s? 
50's?     66f's?     83i's? 


3.  16f  is  what  part  of  50? 

4.  331  is  what  part  of  50  ? 

5.  50  is  how  many   16f's? 

831?     100? 

6.  66f  are  how  many  16|'s? 

7.  83|  are  how  many  16|'s? 

8.  100  is  how  many  16|'s? 

9.  A  man  paid  16|  of  a  dollar  each  for  15  books.     What  did 

they  cost  him? 

10.  A  boy  33|  miles  from  home,  rode  |-  the  distance  on  his 

wheel.     How  many  miles  did  he  ride? 

11.  A  piece  of  cloth  3  yds.  long  sold  for  50^*.    What  was  tlie 

price  per  yd.  ? 

12.  A  girl  picked  66f  qts.  of  berries  in  4  days.     What  was 

the  average  amount  per  day? 

13.  A    hundredweight    of    grain    was    divided    into    6    equal 

amounts.     How  many  pounds  in  each? 

14.  From  a  tank  of  water,  16|  gals,  were  drawn  out,  which 

were   J,   of  the  amount  remaining.      How  many  gallons 
were  left  in  the  tank? 


PART   THIRD.  227 

1.  A  schooner  brought  48,972  spruce  trees  from   iiortlieru 

Michigan  to  Chicago  at  Christmas  time.  What  are  they 
worth  at  90^'  a  dozen? 

2.  A  blacksmith  shoes  42  horses  at  $2  each  in  1  week.     The 

shoes  and  nails  cost  him  §8,  shop  rent  $12,  and  he  pays 
each  o£  his  two  helpers  $15  per  week.  What  was  his 
share  of  the  money  received? 

3.  A  teamster  has  his  two  horses  shod  all  around,  twice  each 

month,  during  December,  January  and  February,  and 
once  a  month  the  remainder  of  the  year.  What  does  it 
cost  a  year  at  $2  per  shoeing  for  each  horse? 

4.  A  cooper  made  1000  butter  tubs  at  12^'  each  and  600  bar- 

rels at  30^/  each.  If  he  paid  J  of  the  price  for  lumber 
and  I  of  it  to  his  workmen,  how  much  did  he  have  left? 

5.  If  each  tub  holds  24  pounds,  what  will   1000  tubs  of  but- 

ter be  worth  at  21^;  per  pound? 

6.  If  each  bbl.   holds  3  bu.  of  apples,  what  will  600  bbls. 

bring  if  sold  at  30^-  per  peck? 

7.  There  are  630  sq.   yds.  of  lathing  needed  in  a  new  house 

and  it  can  be  done  in  6  days.  Will  a  man  earn  more 
by  doing  it  by  the  day  at  $3  per  day  or  by  the  square 
yard  at  3^'  per  sq.  yd.  ? 

8.  If  54  laths  will  cover  4  sq.  yds.  how  many  will  be  needed 

for  600  sq.  yds.?    How  many  bundles  of  50  laths  each? 

9.  If  each  lath  uses  6  nails,  and  54  laths  cover  4  sq.  yds., 

how  many  nails  will  600  sq.  yds.  use?  How  many 
pounds  allowing  400  nails  to  the  pound? 

10.  A  carpenter  works   5|   days  in  a  week  at  $3  per  day,  but 

breaks  a  saw  worth  $1.40  and  loses  a  hammer  worth  90^-. 
What  is  the  week's  work  worth  to  him? 

11.  A  painter  has  3  helpers  at  $3.50  per  day  and  2  at  $3. 

What  must  he  charge  for  a  week's  work  so  as  to  have 
$25  for  himself  ? 


228 


THE   RATIONAL   ARITHMETIC. 


1.  Review  pages  162  and  163. 

2.  What  is  the  name  of  the  first  period? 

3.  AVhat  is  the  name  of  the  second  period  ? 

4.  How  many  places  are  there  in  units'  period? 

5.  Each  period  has  three  places. 

Thousands.  [Tnits. 


en 

^ 

/ 

•o 

'3 

01 

CD 

u 

U 

Tl 

, 

• 

, 

• 

a 

VI 

r/j 

'/• 

13 

<x> 

1— < 

'^ 

rj 

!:3 

W 

H 

O 

y^ 

H 

O 

2  4   ()   ,12  3 
0,   Read    the  figures  of    each   period    as  though  they  stood 
alone  and  then  add  the  name  of  the  period. 

246  thousands. 
123  units,  or  ones. 

7.  If  we  multiply  the   number  246,123  by  10  we  will  have 

the  beginning  of  a  new  period,  2,461,230. 

8.  This  will  be  read: 

2  millions  (this  is  the  name  of  the  new  period). 
461  thousands 
230 

9.  The  use  of  figures  to  represent  numbers,  as  we  have  been 

doing,   is    called    the    Arabic  Notation    or   method  of 
writing  numbers. 

10.  There  is  another  method  of  writing  numbers,  in  which 

letters  are  used.      This  is  the  Roman  Notation. 
11.   Fill  out  the  following  blanks  with  figures: 

XI  =  

L  =  , 

C    =: 

XL  = 

XC  =^  


I  - 

VI  - 

II  - 

VII  - 

III  - 

VIII  = 

IV  - 

IX  - 

V  - 

X  ^- 

12.   What  is   the   equivalent  in   figures   of  I?     V?     X?     L? 
C?     D?     M? 


PART   THIRD. 


229 


1.  If  a  letter  is  followed  by  one  or  more  letters  of  equal  or 

less  value,  the  sum  of  all  is  the  value  of  the  iiumbei 
represented.  Thus:  VI  =  6;  XI  =  11;  XX  =  20; 
CLX  =  160;  DC  =  600. 

2.  If  a  letter  is  followed  by  another  of  greater  value,   the 

difference  of  the  two  is  the  value  of  the  number 
represented.  Thus:  IV  =  4;  IX  =  9;  XIX  =  19; 
XL  =  40;  CD  =  400. 


3. 


Read  the  following  numbers  written  in  the  Roman  Nota- 


tion: 
IV 
XIX 
XXXIV 
XLIX 
XCIX 
CCCXXVI 


VIII 

XVI 

XLIV 

LIV 

CIX 

MCLXXIV 


II 

XIV 
XXVII 
LXIX 
CLXIX 
DIX 


IX 

XXXIX 

XI 

LXXVIII 

LC 

MLV 


4.   Write  the  following  numbers  in  the  Roman  Notation: 


9  = 
4  -: 
7  = 
6  = 
14  = 
29  = 


13  = 

78  =: 

44  = 
83  = 
59  = 
94  = 


96  = 
104  = 
199  = 
335  = 
549  == 
2000  = 


D. 


(Write  answers  to  the  following  in  Roman  numerals.) 
Columbus  discovered  America  in  MCDXCII;    20  years 
later  Florida  was  explored.     In  what  year  was  Florida 
explored  ? 

6.  The    first    battle    of     the     Revolution    was    fought    in 

MDCCLXXV;  the  last  battle  was  fought  6  years  later. 
What  was  the  year  of  the  last  battle? 

7.  Washington   was   elected  President  in  MDCCLXXXIX; 

Lincoln  was  elected  71  years  afterward.     In  what  year 
was  Lincoln  elected? 


o 


30 


THE   RATIONAL   ARITHMETIC. 


Add  the  following: 


(1) 

7843 

(2) 
32765 

(3) 

25987 

(4) 
96875 

(5) 

81818 

(6) 
247 

8789 

89247 

6586 

40984 

92193 

91838 

9576 

76348 

78379 

50839 

87689 

9705 

2589 

20873 

96468 

9787 

76434 

87278 

8956 

94608 

980 

67898 

68979 

3849 

3210 

13495 

20876 

76580 

37590 

89878 

7029 

68950 

67099 

54777 

89763 

79929 

47992 


3    3    4 


In  each  column  the  number  to  be  carried  may  be  indicated  by  placing 
the  figure  immediately  underneath  the  column,  as  in  problem  1. 

To  prove  your  work,  add  the  columns  from  the  top,  downward. 


(') 

68 

(8) 

238 

(9) 

3271 

(10) 

17284 

(11) 
24567 

(12) 

237 

97 

472 

4089 

35873 

89012 

48984 

89 

836 

3765 

89656 

4567 

3789 

43 

980 

2188 

25784 

89876 

54976 

30 

722 

3900 

92375 

54378 

500 

78   405 

146 

4895 

71084 

98989 

3897 

83 

348 

6589 

25874 

24864 

57878 

29 

765 

8077 

39058 

3099 

36498 

48 

897 

9384 

87643 

87655 

9889 

67 

305 

6589 

97979 

98788 

65847 

98 

969 

9283 

86786 

4890 

678 

88   413 

878 

5670 

78978 

86767 

88796 

39 

438 

8023 

27605 

67987 

3480 

64 

765 

9387 

43991 

4389 

27938 

89 

735 

4738 

37642 

97689 

988 

95 

897 

8777 

49877 

9480 

77658 

47   407 

642 

4738 

79988 

84976 

7865 

1225     1225 

1 1  1 

Another  method  of  proof  is  to  divide  the  columns  into  shorter  col- 
umns, add  separately,  as  indicated  in  number?,  and  add  these  separate  sums. 


PART   THIRD. 


231 


6384 
1945 


The  larger  number  is  called  the  Minuend. 


4889 
6834 


The  smaller  number  is  called  the  Snhirahend. 
The  result  is  the  Difference  or  Remainder. 
The  addition  of  the  difference  and  the  subtra- 
hend should  give  the  minuend  and  is  the  Proof. 

2.   Subtract  the  following: 

(1)  (2)  (3)  (4)  (5)  (6) 

8346         24890         36745         48234         57855         72180 

5838         17901         17829         29018         29666         23092 


(7) 

(8) 

(9) 

(10) 

(llj 

(12) 

62387 

83475 

90281 

38297 

27666 

87726 

34299 

56077 

37345 

19088 

18785 

68640 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

418967 

687240 

723485 

868240 

927200 

70724 L 

229875 

478119 

438907 

372906 

418117 

354438 

(10)  (20)  (21)  (22)  (23)  (24) 

381487      592173      600840      821380      727248      917288 
191598      394205      236450      291653      570649      129399 


3.  A  man  began  business  with  $5,275.75;  in   five  years  he 

had  §22,794.50.      How  much  liad  he  gained? 

4.  One  country  road  is  20  mi.  160  rds.  long;  another  is  14 

mi.  80  rds.  long;  how  much  longer  is  the  first? 

5.  A  cotton  dealer  bought  328,900  lbs.  of  cotton  one  year, 

and  715,600  lbs.   the  next.      How  many  more  lbs,  did 
he  buy  the  second  year? 

6.  One  vessel  is  valued  at  $1,250,000;  another  at  ^975,800. 

What  is  the  difference  in  value? 

7.  A  box  containing  43,200  cu.  in.  was  divided  into  two  parts; 

one  holding  25,920  cu.  in.     How  many  cu.  in.  in  the 
second  part? 


232 


THE   RATIONAL  ARITHMETIC. 


1.  Reviow  pages  95  and  173. 

2.  Multiply  892  by  235. 

r  892  X  5 
892  X  235  =  ]  892  X  3  tens 

'  892  X  2  hundreds 
892  The  number  multiplied  is  the  Multiplicand. 
235     The  number  multiplied  by  is  the  Multiplier. 

4460  892  X  5 

2676  892  X  3  tens 

1784  892  X  2  hundreds 

209620     The  result  of  multiplying  is  the  Product. 

It  will  be  noticed  that  the  first  right  hand  figure  of  each  partial  pro- 
duct is  placed  directly  beneath  the  figure  by  which  we  are  multiplying. 
Thus,  when  multiplying  by  3,  the  first  figure  of  the  partial  product,  G,  is 
placed  beneath  and  in  a  line  with  the  3;  and  when  multiplying  by  2,  the  4 
of  the  partial  product  is  placed  directly  beneath  the  2. 

3.  Multiply  729  by  460. 


729  X  460  =  ]  ^^  ^   f^   ^  ^ 

(  729  X  4  hundreds 

729 

460 

43740 

729  X  60 

2916 

729  X  4  hundreds 

335340 
4.  Multiply  476  by  308. 

476  X  308  = 

476 

308 


476  X  8 

476  X  3  hundreds 


3808 
1428 

146608 


476  X  8 

476  X  3  hundreds 


PART   THIRD.  233 

1.  Find  the  following  products: 

573  X  248  384  X  537  735  X  376  487  X  789 

858  X  305  275  X  937  972  X  219  976  X  253 

835  X  583  508  X  607  506  X  429  4005  x  129 

968  X  ()75  651  X  234  309  x  150  2060  X  456 

809  X  584  943  X  923  847  X  907  3070  X  250 

548  X  394  475  X  406  653  X  295  1022  X  284 

2.  An  elevator  in  a  tall  building  goes  up  165  ft.  and  down 

the  same  distance  each  trip.      How  many  feet  does  it 
go  in  152  trips? 

3.  If  it  cost   56^-   per  word  for  a  cablegram  from  Japan  to 

Chicago,  what  is  the  cost  of  a  message  of  1213  words? 

4.  If  a  steamer  burns   378  pounds  of  coal  in  going  1  knot, 

how  many  pounds  will  she  burn  in  going  15,288  knots? 

5.  There  are  40  street  lamps  on  1  mile  of  street,  each  burn- 

ing 18  cu.  ft.  of  gas  every  night.     How  much  gas  will 
they  burn  in  the  month  of  April? 
().   A  library  has  in  one  case  27(^  books,  which  contain,  on  an 
average,  304  pages  each.     How  many  pages  of  reading 
matter  in  the  bookcase? 

7.  There  are  897  hills  of  corn  in  a  single  row  and  364  such 

rows  in  a  field.     How  many  Mils  of  corn  in  the  entire 
field? 

8.  There  are  43,560  square  ft.  in  an  acre.      If  189  pounds  of 

water  fall  on  one  square  ft.  in  a  j-ear,  how  many  pounds 
will  fall  on  an  acre? 

9.  There  are  12  elevators  in  a  builditig.      They  each  make 

94  round  trips  in  a  day  and  carry,  on  an  average,  4 
passengers  each  way.  How  many  passengers  make 
single  trips  on  all  of  them  in  a  day? 
10.  In  a  single  layer  in  a  wall  there  are  964  bricks.  The 
wall  is  197  bricks  high.  How  many  bricks  does  it 
contain  ? 


234  THE   RATIONAL   ARITHMETIC. 

1.  Divide   20,  30,  40,  60,   90,   70,  80,  each  by  10.     In  each 

case  what  do  you  do  when  dividing  by  10? 
Divide  250,  520,  750,  640,  980,  370,  each  by  10. 

2.  Divide  400,  900,   800,   500,   300,  each  by  100.     In  eacli 

case  what  do  you  do  when  dividing  ])y  100? 
Divide  7500,  8900,  2400,  6400,  3700,  each  by  100. 

3.  Divido  7000,  9000,  2000,  8000,  each  by    1000.     In  each 

case  what  do  you  do  when  dividing  by  1000? 
Divide  75000,  26000,  867000,  845000,  each  by  1000. 

4.  Divide  860  by  20. 

The  nunil)er  to  be  divided  (860)  is  called  the  Dividend. 
The  number  to  be  divided  by  (20)  is  called  the  Divisor. 
The  result  of  the  division  (43  below)  is  the  Quotient. 

(  10)860  ) 
20  =^   10  X  2.      Then  860  -^  20  =  <      '2)m  \  =20)860 

(     —43)  43" 

When  the  dividend  and  divisor  both  end  in  a  cipher,  the  cipher 
may  be  canceled  as  above  and  the  division  made  as  indicated  without 
the  ciphers. 

5.  Divide  9200  by  400. 
400)9200 

23 

When  the  dividend  and  the  divisor  end  in  two  or  more  ciphers, 
an  equal  number  of  ciphers  may  be  canceled  from  each  as  above,  and 
the  division  made  as  indicated  without  the  ciphers. 

6.  Divide : 

480  ^  30       3600  --  1200      16000  ~  2000 

720  -^  40       2700  ^  900       21000  --  7000 
540  --  60       6300  -  700       60000  -^  12000 

270  -^  90  13200  -^  1100  25000  -^  5000 

650  -  50       8400  --  400  24000  -  3000 

490  --  70       5000  --  1000  54000  ^  9000 

720  --  80       9300  --  300  36000  --  4000 

780  --  20       6400  ^  800  96000  ^  8000 


PART 

THIRD.                                        231 

1. 

Divide  21,816  by  72. 
303 

72)21816 
216 

216 
216 

• 

2. 

Divide  15,250  by  61. 

3.  Divide  5130  by  342 

250 
61)15250 

15 

342)5130 

122 

342 

305 

1710 

305 

1710 

0 

4. 

Divide  25,215  by  105. 

240AV 

Proof:       105    divisor. 

105)25215 

240  quotient. 

210 

4200 

■421 

210 

420 

25200 

15  rem. 

15  rem. 

25,215  dividend. 
To  prove  the  correctness  of  division,  multiply  the  divisor 
by  the  quotient,  and  add  the  remainder  if  there  be  one. 
The  result  should  equal  the  dividend. 
5.   Divide : 

3767  -^  38  99,684  --  234 

7873  --  41  91,464  --  111 

7692  -^  32  94,770  -^  135 

67,654  --  53  95,928  ^  806 

26,754  -=-  64  90,750  ^  125 


95,637  ^  75 


76,894 


86 


68,331  -^  911 
33,633  --  111 


236  THE   RATIONAL   ARITHMETIC. 

1.  A  lumber  vessel  carried  887,392  barrel  staves.     Allowing 

16  staves  to  the  barrel,  how  many  barrels  can  be  made 
from  them? 

2.  A  ship  traveled  about  15,238  nautical  miles  in  66  days, 

stopping  12  days  on  the  way  for  coal  and  other  sup- 
plies.    What  was  her  average  speed  per  hour? 

3.  The  Danube  Eiver  is  1,725  miles  long,  the  Ehine  600 

miles  and  the  Rhone  580  miles.     How  many  times  as 
long  as  the  Thames,  220  miles,  is  their  united  length? 

4.  There  are  102  counties  in  Illinois  and  the  area  of  th(^ 

state  is  56,650  square  miles.     What  is  the  average  sizu 
of  each  county? 

5.  Chicago's  area  is  119,689  acres.     How  many  square  miles 

of  land  in  Chicago? 

6.  A  field  oE  corn  has  in  it  229,599  hills.     There  are  291 

equal  rows.      Hoav  many  hills  in  each  row? 

7.  A  rectangular  farm  contains  552,866  square  yards.     One 

end  of  it  is  563  yards  long.     How  long  is  one  side? 

8.  A  field  contains  926,156  square  feet.     One  end  of  it  is 

679  feet  long.     How  long  is  one  side? 

9.  At  a  brick  yard  3,276,221  bricks  were  made  during  the 

season.     They  were  hauled  away  in  824  equal  loads. 
How  many  bricks  were  hauled  at  a  load? 

10.  ^48,077.29  was  divided  equally  among  709  men.     How 

much  did  each  receive? 

11.  A  merchant  sold  999  bicycles  for  $41,793.72.     What  was 

the  average  selling  price  of  each  bicycle? 

12.  In  312  days  of  the  year  a  merchant  sold  $91,040  worth 

of  goods.     What  did  his  daily  sales  average? 

13.  In  four  years  a  factory  uses   1,434,160  pounds  of  coal. 

What  was  the  average  amount  used  per  week? 

14.  The  Atlantic  Ocean  in  the  deepest  part  is  27,366   feet 

deep.     What  is  its  depth  in  miles? 


PART    THIRD. 


237 


20 

1 

2 

3 

4 

5 

1. 

2. 
3. 
4. 
o. 

6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 


How  many  20's  in  40? 
40  is  how  many  20's? 
60  is  how  many  20's? 
80  is  how  many  20's? 
100  is  how  many  20's? 


20 
40 
60 
80 
100 


In  80?     60?     100? 
What  part  of  60?     Of  80?     100? 
40's  ?     What  part  of  80  ?     100  ? 
40's?     60's?     What  part  of  100? 
40's?     60's?     80's? 
A  boy  bought  80  papers  for  44^-.    The  next  day  he  bought 

20  papers  at  the  same  rate.      What  did  they  cost  him  ? 
A  train  goes  40  miles  in  55  minutes.     At  the  same  rate 

how  long  will  it  take  to  go  80  miles? 
A  boy  rode  9  miles  in  1  hour.     How  far  will  he  ride  at 

the  same  rate  in  40  minutes? 
60  qts.  of  syrup  cost  ^7.20.     At  the  same  rate  what  will 

5  gal.  cost? 
A  man  puts  20  pounds  of  meal  in  one  sack.     How  many 
sacks  will  he  need  for  1  hundredweight? 


^  of  a  bu.  of  wheat  weighs   20  pounds.     How  many  bu. 

weigh  60  pounds?     80  pounds?     100  pounds? 
A  toy  bank  holds  $2  in  dimes.     How  many  weeks  will  it 

take  to  fill  it  if  20^*  are  put  in  each  week  ? 
Allowing  4  weeks  to  the   month,  how  many  terms  of  20 

weeks  are  there  in  10  months  of  school?     How  many 

terms  does  a  boy  spend  in  school  who  attends  25  school 

months  ? 

14.  It  takes  a  man  20  minutes  to  reach  his  office.     What  part 

of  an  hour  does  it  take  him  each  day  to  go  and  return  ? 
How  many  hours  does  it  take  him  in  6  days  ? 

15.  A  man  bought  40  horses  for  $2880.     At  the  same  rate 

what  will  be  the  cost  of  100  horses  ? 


238  THE   RATIONAL   ARITHMETIC. 


oz. 

=  ounce. 

lb.  =  pound. 

cwt. 

=  hundredweight.           T. 

=  ton. 

lib. 

1  cwt. 

IT. 

16  oz. 

100  lbs. 

20  cwt. 

1.  How  many  ounces  in   8   lbs.  ?     In   14  lbs.  ?     In  20  lbs.  ? 

In  25  lbs.  ? 

2.  How  many  pounds  in  3|-  cwt.  ?     In  7^  cwt.  ?     In  9^  cwt.  ? 

3.  How  many  pounds  in  1  T.  ?     In  4  T.  ?     In  3i  T.  ? 

4.  How  many  ounces  in  ^  cwt.?     In  2|  cwt.?     In  3|  cwt.? 

5.  How  many  ounces  in  |  T.  ?     In  3^  T.  ?     In  2^  T.  ? 

6.  How  many  hundredweights  in  ^  T.  and  in  ^  T.  together? 

7.  1  T.  equals  10  cwt.  and  how  many  pounds? 

8.  Add: 

2  T.  17  cwt.  25  lbs.  1  T.  8  cwt.  60  lbs. 

1  2  75  4       1  40 


10  cwt.  25  lbs.  8  oz. 

9  cwt.  20  lbs.  4  oz 

5          30          6 

4            9          9 

4          44          2 

6          18          2 

9.   Subtract: 

3  T.  15  cwt.  14  lbs.  2  T.  12  cwt.  9  lbs. 


2         7  8  18  6 


i 


15  cwt.  75  lbs.  8  oz.  16  cwt.  43  lbs.  12  oz. 

8  35  5  14  23  8 


10.  Multiply: 

3  T.  5  cwt.  15  lbs.  2  T.  3  cwt.  20  lbs. 

4  5 


2  cwt.  9  lbs.  2  oz.  4  cwt.  3  lbs.  4  oz. 

8  4 


11.  Divide: 

2)4  T.  18  cwt.  50  lbs.  3)6  T.  15  cwt.  48  lbs. 


PART   THIRD.  239 

1.  At  10^  an  oz.  how  much  will  3^  lbs.  of  cinnamon  cost? 

4 J  lbs  ? 

2.  What  will  a  ton  of  hay  cost  at  ^^'  a  pound? 

3.  A  bushel  of  wheat  weighs  60  lbs.     How  many  bushels  in 

a  load  of  wheat  weighing  1  T.,  6  cwt.  and  40  lbs.  ? 

4.  A  family  uses  75  lbs.  of  ice  every  day  for  20  days.     What 

does  it  cost  them  at  35^'  per  cwt.  ? 

5.  From  10  cwt.  of  sugar  a  grocer  sold  8  cwt.,  40  lbs.,  12 

oz.     How  much  was  left? 

6.  60  lbs.,  10  oz.  of  tea  were  divided  equally  among  5  per- 

sons.    How  much  did  each  receive? 

7.  A  man  bought  3  lbs.,  8  oz.  of  meat  at  16^-  a  lb.  and  2  lbs.. 

12  oz.  of  butter  at  20^  a  lb.      What  was  the  total  cost^ 

8.  A  bushel  of  oats  weighs  32  lbs.     How  many  bushels  in 

80  cwt.  ? 

9.  From  a  keg  of  nails  weighing  1  cwt.,  15  lbs.  and  8  oz. 

were  taken  at  one  time,  9  lbs.  and  12  oz.  at  another. 
What  was  the  weight  of  the  remainder? 

10.  How  many  bales  of  cotton,  each  weighing  450  lbs.  may 

be  shipped  on  a  vessel  which  can  carry  2250  tons  ?  On 
a  vessel  that  can  carry  3000  tons? 

11.  What  will  it  cost  to  have  8  tons  of  coal  hauled  at  75^  a 

load  of  3500  lbs.  ? 

12.  500  bbls.  of  flour  are  shipped  in  7   equal   loads.     How 

many  tons  will  each  load  weigh  if  1  bbl.  weighs  196 
lbs.? 

13.  A  man  hauled   8  loads  of  wheat,  35  bu.   at  a  load.     A 

bushel  of  wheat  weighs  60  lbs.  What  was  the  weight 
of  the  8  loads?  How  many  hundredweight  in  each 
load? 

14.  A  farmer  owning  700  bu.  of  oats  sold  9  loads  of  2240  lbs. 

each.  One  bushel  weighs  32  lbs.  How  many  bushels 
had  he  left  ? 


240  THE'   RATIONAL    ARITHMETIC. 


sec.  =  second.                hr.  =  hour. 

wk.  =  week. 

min.  =  minute.              d.  =  day. 

mo.  =  month. 

yr.  =  year. 

1  min.                   1  hr.                      1  d. 

Iwk. 

lyr. 

60  sec.                   60  min.                 24  hr. 

7d. 

12  mo. 
52  wks.  1  d 
365  d. 

1.  Review  page  157. 

2.  How  many  months  in  |-  a  yr.  ?     In  3^  yrs.  ?     In  5  J  yrs.  ? 

3.  How  many  minutes  in  3  lirs.  ?     In  2^  hrs.  ?     In  1^-  hrs.  ? 
In  1^  of  an  hr.  ?     In  one  day  ? 

4.  In  4  yrs.  how  many  days?     In  2-J-  yrs.  ?     In  |^  of  a  yr. ? 

5.  How  many  seconds  in  5  min.  ?     In  one  hr.  ?    In  |-  an  lir.  ? 
In  J  a  day?  ^ 

6.  Add: 

8  hrs.,  30  min.,  15  sec.  3  mo.,  1  wk..  7  d. 

3  29  45  8  3         12 


1  yr.,  8  mo.,  15  d.  2  yrs.,  6  mo.,  10  d. 

3         2  5  2  4  15 

7.  Subtract: 

24  hrs.,  50  min.,  30  sec.  4  yrs.,  8  mo.,  15  d. 

8  30  15  12  6 


6  yrs.,  4  mo.,  20  d.  5  yrs.,  9  mo.,  6  d. 

3  3  12  4  8  5 

§.   Multiply: 

4  lirs.,  15  min.,  30  sec.  3  hrs.,  15  min.,  20  sec. 

2  3 


4  yrs.,  2  mo.,  4  d.  5  yrs.  2  mo.,  3  d. 

5  6 


PART  THIRD.                                      241 

1.  Divide: 

3)6  hrs.,  45  min.,  15  sec.  6)24  hrs.,  30  min.,  18  sec. 

2)4  yrs.,  8  mo.,  12  cl.  5)5  yrs.,  10  mo.,  15  d. 


2.  Find  the  time  between  June  6,  1885,  to  Aug.  12,  1889. 

The  difference  between  dates  is  found  by  subtraction,  using  the  num- 
bers of  the  months  named. 

yr.  mo.  d. 

Aug.  12,  1889  =  1889      8      12 
June  6,  1885  =   1885      6 6^ 

4     2      6 

3.  Find  the  time  from: 

Jan.  2,  1865,  to  June  5,  1887. 
Mar.  12,  1885,  to  May  21,  1889. 
July  21,  1872,  to  Sept.  26,  1890. 
Feb.  15,  1860,  to  Oct.  29,  1878. 
Nov.  2,  1889,  to  Dec.  28,  1892. 
Apr.  10,  1879,  to  Aug.  25,  1897. 

4.  If  a  boy  works  -J  of  each  day  for  6  days  at  20^-  an  hr., 

what  is  his  week's  salary  ?  If  he  Avorks  9  hrs.  overtime, 
half  of  that  time  at  15^/  a  half  hour  and  the  rest  at  20^/ 
a  half  hour,  Avhat  is  his  pay  for  the  extra  work? 

5.  A  man  leaves  his  office  for  home  at  5.45  p.  m. ,  and  arrives 

45  min.  later.  AVliat  time  does  he  reach  home  ?  If  he 
takes  the  same  time  going  and  returning  every  day, 
how  many  hours  does  he  thus  spend  in  ten  days? 

6.  A  fast  mail  train  runs  from  Chicago  to  Burlington  in  5 

hrs.  20  min.  45  sec.  and  a  freight  train  runs  the  same 
distance  in  9  hrs.  40  min.  How  much  longer  does  it 
take  the  freight  train? 

7.  James  was  born  September  18,  1887,  and  Willie  was  born 

December  21,  1892.     How  much  older  is  James? 


24.2  THE.  RATIONAL   ARITH^IETIC. 

1.  There  are  319  pages  in  a  book,  how  many  pages  are  there 

in  369  such  books? 

2.  There  are  18  windows  on  each  side  of  a  car.      How  many 

windows  are  there  in  397  cars? 

3.  In  a  7  story  buikling,  there  are  on  each  of  the  sides,  27 

windows  on  each  story;  there  are  on  each  of  the  ends 
16  windows  on  each  story.      How  many  windows  in  all? 

4.  A  street  paved  with  stone  blocks  contains  65  stones  in 

width  and  786  in  length.  One  man  must  buy  half  of 
these.  If  they  cost  him  7^  each,  how  much  must  he 
pay  for  them? 

5.  How  many  grains  will   1,648  silver  dollars  weigh,  if  one 

dollar  weighs  41 2 A  grains? 

6.  A  man  deposits  -$372  in  the  bank  each  week  day  for  26 

weeks.      How  much  does  he  deposit  in  that  time? 

7.  A  man  rides   116  miles  a  day  on  his  bicycle.     How  far 

from  the  ciify  can  he  go  and  return  in  12  days? 

8.  It  is  195   feet  between  the  telegraph  poles.      How  much 

wire  is  needed  to  put  up  6  wires  on  257  poles? 

9.  A  merchant  bought  97  rolls  of  carpet,  27  of  them  con- 

taining 56  yards  to  the  roll,  34  containing  59  yards  to 
the  roll,  and  the  remainder  63  yards  to  the  roll.  How 
many  yards  did  ho  buy? 

10.  A  manufacturer  sold  65  cases  of  shoes,  each  case  contain- 

ing 6  dozen  pairs,  at  $2.75  a  pair.  What  was  the 
amount  of  his  sale? 

11.  A  farmer  had   2,365  bushels  of  wheat.     He  sold   1,240 

bushels  at  65^  a  bushel,  643  bushels  at  85^  a  bushel, 
and  the  remainder  at  96^  a  bushel.  How  much  did  he 
get  for  the  entire  crop  of  wheat? 

12.  A  merchant's  sales  were  $127  each  day  for  23  days,     $156 

each  day  for  19  days,  and  $113  each  day  for  32  days. 
How  much  were  his  sales  for  the  entire  time? 


PART    THIRD.  243 

1.  It    is   85    miles    from    Chicago    to    Milwaukee.       A  man 

went  from  Chicago  to  Milwaukee  and  returned  each 
day  for  26  days.     How  many  miles  did  he  travel? 

2.  A  man  lived  27  miles  from  Chicago.      He  came  into  the 

city  and  returned  6  days  each  week  for  14  w^eeks.  How 
many  miles  did  he  travel? 

3.  A  manufacturer  sold  687  bicycles  at  $47  each.     How  much 

did  he  get  for  them  ? 

4.  An  agent  sold  163  reapers  at  $145  each.     What  was  the 

amount  of  his  sale? 

5.  The  cost  of  one  car  is  $965.     A  railroad  company  buys 

235  such  cars.      AVhat  is  the  cost  of  the  cars? 

6.  A  square  building  is   115   feet  high   and  122  feet  wide. 

What  is  the  area  of  one  of  its  sides  in  square  feet? 

7.  The  same  building  is  covered  with  a  flat  roof.    How  many 

square  feet  in  the  roof? 

8.  53  cars  stand   in  a  solid  blockade  on  the  street.     26  of 

them  are  32  feet  long  and  the  remainder  37  feet  long. 
How  far  is  it  from  one  end  of  the  blockade  to  the  other  ? 

9.  A   street  car   company   sold  540  horses   at  $62.25  each. 

How  much  did  it  get  for  the  horses? 

10.  A  man  works   8J  hours   a  day,  6  days  in  the  week,  for  26 

Aveeks.     How  many  minutes  does  he  work  ? 

11.  For  every  25   papers  a  boy   delivered   he   received   13^. 

If  he  delivered  at  this  rate  175  papers  a  day  each  week 
day  for  2  weeks,  how  much  money  did  he  get? 

12.  The    school    year    contained    40    weeks.       Each    week   I 

burned  a  quart  of  oil,  which  cost  me  13^  a  gallon. 
What  did  my  oil  cost  me  for  the  school  year? 

13.  An  elevator  boy  received  $13  a  month  as  wages.     At  the 

end  of  the  year  he  had  spent  $19  for  clothing,  $32  for 
car  fare,  $4.50  for  books  and  had  given  his  mother  $48. 
How  much  money  did  he  have  left? 


244  THE   RATIONAL   ARITHMETIC. 

1.  Review  page  80. 

2.  A  man  had  in  his  pocket  one  five-dollar  bill,  two  two- 

dollar   bills,   three    one-dollar    bills,   two  half    dollars, 
three  quarters,  four  dimes,  six  nickels  and  three  pen- 
nies.    How  can  he  make  even  change  for  any  one  of 
the  following  purchases: 
8.  A  hat  at  $2.65  and  a  necktie  at  50^'? 

4.  A  vest  at  $3.50  and  a  dozen  collars  at  95^? 

5.  One  book  at  $1.25  and  another  at  38^? 

0.   A  box  of  paper  at  50^',  and  inkstand  at  65^/  and  a  fountain 
pen  at  $1.95? 

7.  A  pair  of  shoes  at  $2.95? 

8.  Railroad  fare  at  14.42? 

9.  Hotel  bill  for  2 J  days  at  $2.50  a  day? 

10.  A  magazine,  35^' ;  a  newspaper,  2^/,  and  a  sheet  of  paper, 

envelope  and  stamp,  5^/? 

11.  A  bicycle  suit  at  Id  70? 

12.  Repairing  bicycle,  $4.70? 

13.  A  boy  went  to  the  bank  to  get  change,  at  various  times, 

for  the  following  amounts.     How  many  of  each  piece 
of  money  might  be  given  him? 

14.  A  twenty-dollar  bill   so  as  to  get  five-dollar  bills,   one- 

dollar  bills  and  half  dollars? 

15.  A  ten-dollar  bill,  so  as  to  get  two-dollar  bills,  one-dollar 

bills,  half  dollars  and  quarters? 
IG.   A  five-dollar  bill,  so  as  to  get  dollars,  half  dollars,  quar- 
ters and  dimes? 

17.  A  two-dollar  bill,  so  as  to  get  half  dollars  and  dimes? 

18.  A  one-dollar  bill,  so  as  to  get  quarters,  dimes,  nickels  and 

pennies  ? 

19.  A  half  dollar,  so  as  to  get  dimes,  nickels  and  pennies? 

20.  A  quarter,  so  as  to  get  pennies,  nickels  and  any  other  coin 

that  he  could  get? 


PART    THIRD.  245 

24  sheets  —  one  quire.  20  quires  =  one  ream. 

1.  How  many  sheets  in  ^  a  quire?     In  f  of  a  quire? 

2.  How  many  sheets  in  J  of  a  ream  ?     In  2  reams  ? 

3.  How  many  quires  in  72  sheets?     In  96  sheets?     In  240 

sheets  ? 

4.  "What  is  the  cost  of  a  quire  of  paper  at  2^*  a  sheet? 

5.  What  is  the  cost  of  a  ream  of  paper  when  bought  at  V> 

sheets  for  1^? 

6.  A  man  bought  1   box  of  paper  containing   2  quires  ajid 

another  containing  5  quires.  How  many  sheets  of 
paper  did  he  get? 

7.  If  12  sheets  of  paper  cost  5^*,  what  is  the  cost  of  a  ream 

at  the  same  rate? 

8.  I  paid  $1.20  for  a  ream  of  paper.      What  was  the  cost  of 

^  a  quire? 

9.  How  many  boxes  will  hold  a  ream  of  paper  if  each  box 

contains  IJ  quires?     IJ  quires? 

10.  A  man  bought  paper  at  $1.50  a  ream   and  sold  it  at  12 

sheets  for  5^/.     How  much  did  he  gain  ? 

11.  A  man  bought  paper  at  $2.75  a  ream  and  sold  it  at  20^-  a 

quire.  What  was  his  gain  ?  If  he  had  paid  §3  a  ream 
and  sold  it  at  25^*  a  quire,  how  much  more  would  he 
have  gained? 

12.  A  ream  of  paper  is  divided  into  40  equal  parts.     What 

part  of  a  quire  is  each? 

13.  Prom  3  reams  of  paper  1 J  reams  were  sold  at  one  time  and 

3  quires  at  another  time.  How  many  sheets  remained? 
How  many  quires?  What  part  of  a  ream? 
14  After  collecting  damaged  lots  of  paper,  a  man  found  he 
had  18  quires  and  10  sheets  of  one  kind,  11  quires 
and  5  sheets  of  another  kind,  and  10  quires  and  5 
sheets  of  a  third  kind.  He  sold  it  at  $1.25  a  ream. 
What  did  he  get  for  all? 


246  THE   RATIONAL   ARITHMETIC. 

1.  A   man  leaves  his  home   each  week  day   at  8.11  in  the 

morning  and  reaches  his  office  at  8.27.  He  returns  in 
the  evening,  leaving  his  office  at  5.45  and  reaching  his 
home  at  6.01.  How  many  hours  does  he  spend  on  the 
way  in  a  Aveek?  In  the  month  of  January,  i£  there  are 
4  Sundays  in  a  month? 

2.  A   teacher   leaves   her   home   each   morning   at   8.20   and 

reaches  the  school-house  at  8.47.  She  returns,  leaving 
the  school-house  in  the  evening  at  3. 48  and  reaching 
her  home  at  4.05.  How  many  hours  does  she  spend  on 
the  way  in  4  weeks?  How  many  hours  in  the  school 
year  if  there  are  38  weeks  of  school  in  a  year? 

3.  How  far  does  she  travel  in  4  weeks  if  the  school-house  is 

1^  of  a  mile  from  her  home?  How  far  does  she  travel 
in  a  school  year  of  40  weeks? 

4.  A   train   leaves  St.   Louis  at   11.31  in   the   evening   and 

reaches  Chicago  at  8  o'clock  in  the  morning.  It  stops 
11  minutes  at  stations  on  the  way.  AVhat  is  the  actual 
running  time  from  St.  Louis  to  Chicago? 

5.  A  train  leaves   Chicago  at  9  o'clock  in  tlie  evening  and 

arrives  in  St.  Louis  at  7.28  the  next  morning.  Another 
train  leaves  Chicago  at  11.30  in  the  evening,  reaching 
St.  Louis  at  8.04  next  morning.  In  how  much  less 
time  does  one  train  run  than  the  other,  and  which  is 
the  faster  train? 

0.  A  train  leaves  Chicago  at  6.30  in  the  evening  and  reaches 
Omaha  at  8.15  next  morning.  If  23  minutes  are  spent 
in  stopping  at  stations,  what  is  the  actual  running  time 
from  Chicago  to  Omaha? 

7.  A  second  train  leaves  Chicago  at  10.30  in  the  evening 
and  reaches  Omaha  at  4  o'clock  the  next  afternoon. 
How  much  longer  is  this  train  on  the  way  than  the  one 
which  left  Chicago  at  6.30? 


PART   THIRD.  247 

1.  If  a  block  containing  3  A.  is  20  rods  wide,  how  long  is  it? 

If  it  contains  10  lots,  how  many  square  rods  in  each? 

2.  A  lot  cost  ^200,  the  house  cost  124^  times  as  much  as  the 

lot,  and  the  fence  ^  as  much  as  the  lot.  What  did  the 
house  and  the  fence  together  cost? 

3.  The  battle  of   Lexington  was   fought   April   19tli,   1775. 

How  many  Aprils  have  there  been  from  then  to  the 
present  day? 

4.  The  buildings  for  the  Columbian  Exposition  were  dedi- 

cated October  12th,  1892.  How  many  years,  months 
and  days  since  then? 

5.  Nathaniel  Hawthorne  was  born  July  4th,  1809,  and  Texas 

was  admitted  to  the  Union  July  4th,  1845.  What  was 
Hawthorne's  age  in  months,  when  Texas  became  a  state? 

6.  Daniel  Webster  was  born  January  18tli,  1782,  and  James 

A.  Garfield  was  born  November  19th,  1831.  How  old 
was  Webster  when  Garfield  was  born? 

7.  Memorial  Day  was  first  celebrated  by  order  of  John  A. 

Logan,  May  30th,  1868,  and  he  was  then  42  years,  3 
months  and  21  days  old.     When  was  he  born? 

8.  Gen.  Grant  was  born  April  27th,  1822,  and  was  41  years, 

2  months  and  7  days  old  when  Yicksburg,  Miss,,  was 
captured.      When  did  he  capture  Yicksburg? 

9.  Gen.  AYm.  T.  Sherman  was  born  Feb.  8th,  1820,  and  fin- 

ished his  great  march  through  Georgia  December  13th, 
1864.     How  old  was  he  on  that  day? 

10.  Gen.  Sheridan  Avas  born  March  6th,  1831,  and  made  his 

famous  ride  from  Winchester  to  the  battlefield  at  Cedar 
Creek,  October  19th,  1864.     What  was  his  age  then? 

11.  Tlie  area  of  Illinois  is   56,650  square  miles  and  the  area 

of  the  Philippine  Islands  is  114,326  square  miles. 
How  much  more  than  twice  as  large  as  Illinois  are  the 
Philippines  ? 


248  THE   RATIONAL   ARITHMETIC. 

1.  A  grain  dealer  bought  25,000  bu.   of  wheat  at  97^'   per 

bushel,  and  after  3  months  sold  it  for  $1.12  per  bu. 
He  paid  storage  charges  at  the  rate  of  -J^-  per  bu.  each 
month.      What  was  his  gain  ? 

2.  A  grain  elevator  holds  800,000  bu.     If  it  is  kept  full  for 

6  months,  what  will  storage  charges  amount  to  at  ^^• 
per  bu.  each  month? 

3.  Six  vessels  carry  800,000  bu.  of  grain  from  Chicago  to 

Buffalo.  If  2  of  them  carry  160,000  bu.  each,  what  is 
the  average  load  of  the  other  four? 

4.  Wheat  weighs  60  lbs.  to  the  bushel.     What  is  the  weight 

in  T.  of  160,000  bu.  ?     In  cwt.  ? 

5.  At  6^/  per  cwt.  what  does  it  cost  to  ship  120,000  bu,  of 

wheat  from  Chicago  to  Buffalo? 

6.  An  elevator  containing  645,000  bu.  of  grain  caught  fire 

and  the  grain  was  damaged.  The  grain  was  worth 
87^  ]:>er  bu.  and  was  insured  for  $250,000.  What  was 
the  loss  ? 

7.  The   owner   of   the  grain,  after   receiving   the   insurance 

money,  sold  the  damaged  grain  for  feed  at  13^'  per 
bushel.     What  was  his  actual  loss? 

8.  Corn  weighs   56   pounds   to  the  bushel.     How  many  car 

loads  of  15  tons  each  will  fill  a  vessel  that  can  carry 
90,000  bu.  ? 

9.  At  10^/'  per  hundredweight,  what  will  it  cost  to  ship  90,000 

bu.  of  corn  from  Chicago  to  New  York  City? 

10.  A  vessel   owner   agrees   to    carry  125,000  bu.  of  corn  for 

$3750.  How  much  does  he  receive  per  hundred- 
weight ? 

11.  A  builder  received  $127.25  for  making  some  repairs  to  a 

house.  He  pays  his  2  helpers  $2.50  each  per  day  for 
the  12  days  needed  to  do  the  work.  AVhat  is  his  own 
share  of  the  money  ? 


PART    THIRD.  249 

1.   How  many  caps  worth  33^^  each,  can  be  bought  for  §15? 

For  $24? 
-.   If  the  price  of  bread  is  raised  from  5^*  to  6^  per  loaf,  how 

much  more  will  700,000  loaves  cost? 
H.   If  a  barrel  of  flour  will  make  196  loaves  of  bread,  how 

many  barrels  are  required  to  make  700,000  loaves? 

4.  A  rapid-fire  gun  shoots  100  shells  per  minute,  how  many 

shells  will  7  such  guns  shoot  at  the  same  rate  in  ^- 
a  minute?     In  1^  minutes? 

5.  If  each  shell  weighs  1  lb.,  how  many  guns  will  it  take  to 

fire  a  ton  of  shells  in  1  minute? 
G.  If  each  shell  uses  up  6  ounces  of  powder,  how  much  pow- 
der will  be  used  by  15  guns  in  1  minute? 

7.  A  man  earning  §1.20  per  day  works  11  days  in  January, 

17  days  in  February,  28  days  in  March,  and  25  days 
in  each  of  the  next  three  months.  How  much  does  he 
earn  in  the  six  months? 

8.  A  man  working  for  $12  per  week  puts  in  J  of  a  day  over- 

time each  day,  for  which  he  receives  double  pay.  How 
much  does  he  earn  in  4  weeks  if  he  works  every  work- 
ing day? 

9.  What  will  the  bricks  for  a  wall  39  ft,  high  cost  at  §5.25 

per  thousand,  if  one  thousand  bricks  will  carry  up  the 
wall  6  in.  ? 

10.  A  brick  mason  earning  50^'  per  hour,  works  7  hours  on 

Monday,  5  hours  on  Tuesday,  and  full  time  —  8  hours 
a  day  —  for  the  rest  of  the  week.  What  is  his  pay  for 
the  week? 

11.  A  gang  of  20  men  digging  for  a  foundation  are  stopped 

by  rain  from  half  past  9  to  a  quarter  past  10  o'clock. 
If  they  are  working  for  20^'  per  hour  each,  how  much  pay 
does  each  one  lose?  How  much  would  they  all  lose  at 
25^'  per  hour? 


350 


THE   RATIONAL   ARITHMETIC. 


%'■ 

'/, 

L- 

F 

B 


G 


w 

c 


D 


— „ — 

II 

:■' ..."         ! 

./W'V 

//•,/'/'■/ 

, 

^%>^< 

E 


" 

J 


*<fe 


» 


1.  Into  how  many  parts  is  A  divided,  and  what  is  one  part 

called? 

2.  How  many  parts,  and  what  is  one  called,  in  B?     C?     D? 

E?     F?     G?     H?     I?     J? 

3.  One  part  of  A  equals  how  many  parts  of  B?     C?     D? 

E?     G?     I?     J? 

4.  One  part  of  F  equals  how  many  parts  ofG?    H?    I?    J? 

D?     E? 

5.  The  number  below  the  line  of  a  fraction  is  the  denom- 

inator, and  indicates  into  how  many  equal  parts  any- 
thing is  divided.  Thus,  as  one  of  the  parts  of  B  is  -J-, 
the  denominator,  ^,  shows  that  B  is  divided  into  4 
equal  parts;  as  one  part  of  G  is  |,  the  denominator,  -g^, 
shows  that  G  is  divided  into  6  equal  parts;  etc. 

6.  The  number  above  the  line  is  tlie  numerator,  and  indicates 

how  many  parts  are  taken.  Thus,  in  f  of  B,  the  numer- 
ator, ^,  shows  that  2  of  the  4  equal  parts  are  taken;  in 
I  of  G,  the  numerator,  -^,  shows  that  2  of  the  6  equal 
parts  are  taken;  etc. 


^  and  ^? 


and 


2T 


7.  What  is  the  sum  of  \  and  W 

4-  and  ^  ?     ^  and  y^  ? 

8.  How  did  you  add  \  and  -|^? 

9    It  has  already  been  seen  that  fractions,  in  order  to  be 
added,  must  have  the  same  denominator. 


PART   THIRD.  251 

1.  Can  you  add  4  a-iid  ^? 

2.  In   |-  there    are    liow  many  |'s?       In  ^   there    are    how 

many  -J's? 

3.  How  many  ^'s  are  t]iere  in  ^  and  J-  together? 

4.  What  is  the  difference  between  i^  and  ^? 

5.  What  is  the  difference  between  |-  and  -J  ? 

6.  What  is  the  difference  between  ^  and  |  ? 

7.  What  is  the  difference  between  |-  and  ^? 

8.  What  is  the  sum  of  4 ,  -§  and  -J  ? 

9.  What  is  the  sum  of  ^,  J  and  ^? 

10.  What  is  the  sum  of  -|  and  l? 

11.  What  is  the  sum  of  J  and  ^? 

12.  What  is  the  sum  of  I,  ^  and  J  ? 

13.  AYhat  is  the  difference  between  ^  and  -^? 

14.  What  is  the  difference  between  ^  and  ^  ? 

15.  What  is  the  difference  between  ^  and  |?     Between  |  and 

I?     Between  |^  and  |^?     Between  |  and  ^?     Between 
I  and  ^? 
IH.   If  J  of  a  yard  of  ribbon  costs  21^',  what  is  tiie  cost  of  ^  of 
a  yard?     The  cost  of  |   of  a  yard  equals  what  part  of 
the  cost  of  I  of  a  yard? 

17.  John  worked  ^  of  the  day  Monday,  f  of  the  day  Tues- 

day, and  l  of  the  day  Wednesday.  How  many  days  did 
he  work  altogether? 

18.  A  girl  having  J  of  a  yard  of  ribbon  bought  |  more.    What 

part  of  a  yard  had  she  then? 

19.  If  from  J  of  a  gallon  of  milk  ^  of  a  gallon  is  taken,  what 

part  of  a  gallon  is  left? 

20.  A  boy  studied  14-  hours  Monday,  1^  hours  Tuesday,  and 

1^  hours  Wednesday.  How  long  did  he  study  during 
the  three  days?  How  much  longer  Monday  than 
Tuesday?  How  much  longer  Wednesday  than  either 
Monday  or  Tuesday? 


252  THE   RATIONAL  ARITHMETIC. 

1.  If  -|  of  a  yard  of  cloth  cost  $.96,  how  much  will  -J   of  a 

yard  cost? 

2.  A  girl  walked  f  of  a  mile,  and  after  resting  walked  -J  of  a 

mile  farther.      What  part  of  a  mile  did  she  walk  in  all  ? 

3.  A  man  traveled  1^  miles  east,  returned,  and  then  went  | 

a  mile  west.     How  far  did  he  travel? 

4.  From  a  piece  of  cloth  24|-  yds.  long,  6|-  yds.  were  sold  to 

one  customer  and  8  J  yds.  to  another.     How  many  yards 
remained? 

5.  One  box  weighs  5|-  lbs.,  a  second  box,  3  times  as  much  as 

the  first,  and  a  third,  ^  as  much  as  the  second.      What 
is  the  weight  of  the  second  and  the  third  box? 

6.  A  family  uses  3 j  cwt.   of  ice  one  week,  2^  cwt.  the  next 

week.     How  much  do  they  use  in  the  2  weeks? 

7.  How  many  jars  holding  ^  of  a  gal.  each  can  be  filled  from 

3 1  gals,  of  water? 

8.  A  boy  attends  school  |   of  the  yr. ;  |-  of  his  vacation  is 

spent  in  the  country.      What  part  of  the  year  does  he 
spend  in  the  country? 

9.  A   grocer   having   4|-   crates   of  berries  sold  |-  of   them. 

How  many  had  he  left? 

10.  A  milkman  sells  |-  of  a  pt.  of  cream  and  l^   qts.  of  milk 

a  dav  to   each   of   2  families.     How  much   cream   does 
he  sell  to  both  in  four  days  ?     How  much  milk  ? 

11.  One  girl  was  absent  from  school  -|^  of  a  month;  another 

girl  was  absent   |-  as  long.      What  part  of  the  month 
was  the  second  girl  absent  ? 

12.  How  many  bean  bags,  each  requiring  J  of  a  yd.  of  cloth, 

can  be  made  from  ^  of  a  yd.  ?     From  -I-  a  yd.  ?     From 
f  of  a  yd.  ?     |-  of  a  yd.  ? 

13.  A  man  when  traveling  spent  |-  of  a  yr.  in  England;   |-  of 

a  yr.  in  France,  |  of  a  yr.  in  Germany,  and  |-  of  a  yr. 
in  Italy.     How  many  yrs.  in  all  ? 


PART   THIRD.  253 

1.  A  woman  bought  4^  qt.   of   berries,  S^  qt.   of  currants, 

and  2^  qt.  of  cherries.  How  many  quarts  of  fruit  did 
she  buy? 

2.  In  making  a  garden,  a  man  planted  -^  A.  in  cabbages,  ^  A. 

in  peas,  y^g  A.  in  beans,  and  ^2  ^-  i^  tomatoes.  How 
much  land  did  he  plant  in  all? 

3.  A  girl  spent  ^-  of  the  summer  in  the  country,  ^  of  it  in 

the  mountains,  and  the  rest  of  it  at  home.  AVhat  part 
of  the  summer  was  she  at  home? 

4.  While   canning   peaches,   a  woman   cut   12   peaches   into 

halves  and  12  into  thirds.  How  many  halves  were 
there?  How  many  thirds?  How  many  more  thirds 
than  halves?  How  many  thirds  equal  four  halves? 
Six  halves  ?     Eight  halves  ?     Ten  ?     Twelve  ? 

5.  A  man  traveled  I  of  a  certain  distance  by  boat,  ^-  by  train, 

and  walked  ^  the  remaining  distance.  What  part  of 
the  distance  did  he  walk? 

6.  From  a  lot  of  5|^  doz.  pairs  of  shoes,  2|-  doz.  were  sold  at 

one  price,  and  the  rest  at  another  price.  How  many 
dozen  were  sold  at  the  second  price? 

7.  A  man  built  4|-  yd.  of  fence  one  day  and  1^  yd.  less  the 

next.     How  many  yards  did  he  build  the  second  day  ? 

8.  The  area  of  a  building  was  30]  sq.  yd. ;  an  addition  J-  as 

large  as  the  building,  was  made.  What  was  the  area 
of  the  addition? 

9.  How  many  square  feet  of  tile  will  be  needed  for  the  floors 

of  two  rooms,  each  containing  18^  sq.  ft.  ? 

10.  A  boy  spent  f  of  every  year  at  college,  for  4  years.     How 

much  time  did  he  spend  there  in  all? 

11.  A  carpenter  bought  528  ft.  of  lumber,  used  -|-  of  it,  sold  ^ 

of  the  remainder,  and  stored  what  was  left.  What  part 
did  he  sell  ?  What  part  did  he  keep  ?  How  many  feet 
did  he  keep? 


rd. 

yd. 

ft. 

in. 

3 

2 

8 

4 

1 

4 

3 

2 

6 

2 

1 

0 

0 

2 

1 

254  THE   RATIONAL   ARITHMETIC. 

1.  Add  8  yd.  2  ft.  8  in.,  4  yd.  1  ft.  4  in.,  and  3  yd.  2  ft.  6  in. 

Write  the  numbers  in  columns,  put, 
ting  m.  under  in.,  ft.  under//.,  etc. 

Add  the  first  right  hand  column 
which  gives  18  in.  But  18  in.  =  1  ft. 
and  6  in.  Write  the  6  in  its  column 
and  add  the  1  ft.  to  the  sum  of  the  col- 
umn of  feet,  which  gives  6  ft.  =  2  yd. 
Write  a  cipher  in  the  column  of  ft. 
and  add  the  2  yd.  to  the  sum  of  the 
column  of  yd.,  which  gives  12  yd.  =  2 
rd.  and  1  yd. 
2    Subtract  2  yd.  2  ft.  8  in.  from  4  yd.  1  ft.  10  in. 

Write  the  numbers  as  in  addition,  and 
subtract;  10  in.  —  8  in.  =  2  in. 

2  ft.  cannot  be  subtracted  from  1  ft., 
X       2         2  so  change  4  yd.  and  1  ft.  to  3  yd.  and  4 

ft.,  and  then  subtract. 
3.  Midtiply  1  yd.  2  ft.  5  in.  by  3. 

Multiplying  through  we  get  3  yd.  6  ft. 
and  15  in.,  which  when  reduced  is  5  yd. 
1  ft.  3  in. 

5       13 

2  1 

Divide  7  yd.  2  ft.  8  in.  by  2. 

s-      -. ^yj7 —. —  Notice    that    the    quotient    is 

placed  above  the  dividend,  each 
unit  in  its  proper  column. 

The  division  is  made  as  usual, 
^  the  remainder  being  changed  to 

^ the   next    lower   unit  and  added 

1   —   12  to   the  number  in   that   column 

20  Then  proceed  as  before. 


yd. 

ft. 

in. 

"3: 

1 

10 

2 

2 

8 

yd- 

ft. 

in. 

1 

2 

5 

3 

0 

1"=     3 


PART   THIRD.  255 

1.  Add  12  sq.  yd.,  4  sq.  ft.,  120  sq.  in.;  4  sq.  yd.,  7  sq.  ft, 

20  sq.  ill.;  0  sq.  yd.,  9  sq.  ft,  16  sq.  in.;  7  sq.  ft,  4 
sq.  in. 

2.  Add  4  cu.  yd.,  9  cu.  ft,  1200  cu.  in. ;  3  cu.  yd.,  400  cu.  in. ; 

4  cu.  ft,  600  cu.  in. ;  5  cu.  yd.,  12  cu.  ft 

3.  Add  15  gal.,  3  qt,  1  pt,  3  gi. ;  4  gal.  2  qt ;  6  qt,  1  pt, 

2  gi.;  9  gal.,  1  pt,  3  gi. 

4.  Add  3  bu.,  3  pk.,  7  qt,  1  pt. ;  4  bu.,  2  pk.,  6  qt ;  3  pk,  4 

qt,  1  pt ;  3  bu.,  1  pk.,  6  qt. ;  1  pk.,  2  qt,  1  pt 

5.  Add  2  T.,  16  cwt,  80  lb.,  8  oz. ;  1  T.,  8  cwt.,  15  lb.,  6  oz. ; 

3  T.,  10  cwt,  50  lb.,  8  oz. ;  18  cwt,  90  lb.,  4  oz. 

6.  Add  4  lir.,  45  min.,  15  sec;  6  lir.,  30  min. ;  55  rnin.,  45 

sec;  3  lir.,  30  sec 

7.  Subtract  16  sq.  yd.,  7  sq.  ft,  44  sq.  in.,  from  24  sq.  yd., 

5  sq.  ft,  120  sq.  in. 

8.  Subtract  3  cu.  yd.,  9  cu.  ft,  680  cu.  in.,  from  12  cu.  yd., 

6  cu.  ft,  1240  cu.  in. 

9.  Subtract  1  gal.,  3  qt.,  1  pt,  3  gi.,  from  4  gal.,  2  qt,  1  pt, 

1  gi. 

10.  Subtract  2  bu.,  2  pk.,  5  qt,  1  pt,  from  6  bu.,  3  pk.,  4  qt  , 

1  pt. 

11.  Subtract  2  T.,  15  cwt,  15  lb.,  9  oz.,  from  4  T.,  12  cwt  , 

20  lb.,  8  oz. 

12.  Multiply  9  cu.  yd.,  8  cu.  ft.,  640  cu.  in.,  by  4. 

13.  Multiply  6  gal.,  3  qt,  1  pt,  3  gi.,  by  5. 

14.  Multiply  5  bu.,  3  pk.,  7  qt,  by  2. 

15.  Multiply  2  T.,  10  cwt,  60  lb.,  12  oz.,  by  3. 

16.  Multiply  4  lir.,  40  min.,  30  sec,  by  5. 

17.  Divide  16  sq.  yd.,  3  sq.  ft,  141  sq.  in.,  by  3. 

18.  Divide  19  cu.  yd.,  1  cu.  ft,  216  cu.  in.,  by  9. 

19.  Divide  26  gal.,  3  qt,  2  gi.,  by  6. 

20.  Divide  12  bu.,  1  pk.,  3  qt,  by  5. 

21.  Divide  12  T.,  3  cwt,  50  lb.,  by  10. 


256  THE   RATIONAL   ARITHMETIC. 

1.  A  train  traveled  32  mi.,  120  rd.,  7  yd.,  one  hour,  and  30 

mi.  160  rd.,  4  yd.,  the  next.  -How  far  did  it  travel  in 
the  two  hours? 

2.  A  man  built  4  yd.,  1  ft.,  8  in.,  of  walk  at  one  time,  and  8 

yd.,  2  ft,  0  in.,  at  another.      How  much  did  he  build? 

3.  One  field  contains  6  A.,  80  sq.  rd.,  and  40  sq.  yd. ;  the  field 

beside  it  contains  14  A.,  120  sq.  rd  ,  20^  sq.  yd.  If 
the  fields  are  joined  into  one,  how  jnuch  land  will  it 
contain  ? 

4.  A  building  whose  area  is  30  sq.  yd.,  6  sq.  ft.,  72  sq.  in.,  is 

enlarged  by  an  addition  whose  area  is  9  sq.  yd.,  8  sq. 
ft.,  72  sq.  in.     What  is  the  area  of  the  entire  building? 

5.  One  room  contains  185  cu.   yd.,   7  cu.   ft.,  192  cu.  in.  of 

air;  another  172  cu.  yd.,  4  cu.  ft.,  432  cu.  in.;  a  third 
864  cu.  yd.,  2  cu.  ft.,  192  cu.  in.  If  the  air  in  all  the 
rooms  is  entirely  changed  once  every  hour,  how  much 
air  will  be  required  in  1  hour? 

6.  Before  buying,  a  grocer  had  2  gal.,  2  qt.,  1  pt.  of  vinegar; 

he  purchased  7  gal.,  3  qt.,  1  pt.  more.  How  much  had 
he  then  ? 

7.  A  farmer  raised  56  bu.,  3  pk.  of  Irish  potatoes,  and  24 

bu.,    2    pk.    of    sweet    potatoes.      How   many   had   he 
in  all? 

8.  One  family  used  1  T.  13  cwt.  50  lb.  of  ice  in  one  summer, 

another  family  used  1  T.  9  cwt.  75  lb.  How  much  did 
they  both  use? 

9.  A  steamship  made  the   first   half  of  a  trip  in  6  d.  10  hr. 

45  min.  and  the  return  trip  in  7  d.  3  hr.  15  min.  If  2 
d.  6  hr.  30  min.  were  spent  in  port  before  returning,  in 
what  time  did  the  ship  make  the  entire  trip? 
10.  A  boy  rode  10  mi.  80  rd.  4  yd.  in  1  hour,  and  2  mi.  120 
rd.  3  yd.  less  the  next  hour.  How  far  did  he  ride  the 
second  hour? 


PART   THIRD.  257 

1.  A  man  owning  a  farm  of  740  A.  and  78  sq.  rd.  sold  290  A. 

and  98  sq.  rd.     How  large  was  his  farm  then? 

2.  In  a  bin  holding  7  en.  yd.  9  cu.  ft.  576  en.  in.   a  partition 

was  plaeed  separating  a  part  holding  3  en.  yd.  18  cu.  ft. 
1152  cu.  in.  What  were  the  contents  of  the  remaining 
part  ? 

3.  From  a  cistern  holding   10  bbl.    14  gal.  1  qt.  of  water,  a 

quantity  was  taken  out,  leaving  2  bbl.  8  gal.  3  qt.  in 
the  cistern.     How  much  was  taken  out? 

4.  A  grocer  bought   12  bu.  1  pk.  of  potatoes  and  4  bu.  3  pk. 

less  of  apples.     How  many  apples  did  he  buy? 

5.  From  a  load  of  grain  weighing   2  T.  14  cwt.  30  lb.,  1  T. 

18  cwt.  80  lb.  were  removed.  What  was  the  weight  of 
the  remaining  part? 
().  One  train  made  a  trip  in  14  lir.  15  min.  25  sec. ;  another 
train  made  the  same  trip  in  1  hr.  50  min.  45  sec.  less 
time.  In  what  time  was  the  trip  made  by  tlie  second 
train  ? 

7.  Two  boats  left  the  same  port  at  the  same  time,  one  sailed 

21  mi.  5^  yd.  while  the  second  sailed  twice  as  far.  How 
far  did  the  second  one  sail? 

8.  A  building  whose   area  was   27   sq.  yd.  3  sq.  ft.  72  sq.  in. 

was  torn  down  and  another  built  whose  area  was  three 
times  that  of  the  old  one.  What  was  the  area  of  the 
new  building? 

9.  In  digging  a  cellar,  24  cu.  yd.  3  cu.  ft.  576  cu.  in.  of  earth 

were  excavated;  it  was  then  determined  to  make  the 
cellar  three  times  as  large.  How  much  more  earth  was 
removed?  How  much  in  all? 
10.  A  book  dealer  shipped  3  boxes  of  books.  One  weighed  1 
cwt.,  90  lb.,  8  oz. ;  the  second  weighed  twice  as  much 
as  the  first,  and  the  third  as  much  as  both  the  others 
together.     What  was  the  weight  of  each? 


258 


THE   RATIONAL   ARITHMETIC. 


(copy  of  bill.) 


ru/  I,    I8C|8 

Bought  of  JOHN  SAMPLE,  BOOKSELLER 


3 

OdAMAAAy 

@  .35 
@  .  0 
@  .05 

$ 

05 
9.0 
9,0 

) 

cJoto/L 

45 

(copy  of  receipted  bill.) 


rrLu:).-/ca^  Cxi/Yxxv  b^curw, 

Bought  of  PRINCE'S  TOY  STORE 


2 
3 


[TlvULA^.X?y  Do-00 

.54 


0 


■  ooXxxL 


S 


2 


lo 


38 

35 


5 


PART   THIRD. 


259 


Copy,  find    amounts    due  on  the    following    accounts,   and 
recei  pt. 

J.  Manning, 

In  account  witli  1).  L.   Parmer,  Dr. 

1898. 


an. 


u 


li 


O         r 


7 


To  75  lbs.  Kice 


'^   330  lbs.  Sugar 


■'    50  lbs.  Java  Coffee 


45  lbs.  Tea 


@  I  .04 

@  .05 

@  .32 

@  .60 


Amount  due, 


James  Oilman, 

In  account  with  Geo.  Johnson,  Dr. 

1898. 


May 

6 

To  5  Days'  Work 

@ 

$2.50 

a 

13 

"   12  lbs.  Nails 

@ 

.03 

(( 

14 

"    7  Panes  of  Glass 

@ 

.40 

June 

11 

'"    10  gals.  Paint 

@ 

1.00 

n 

18 

"    Job  Work  on  House 
Amount  due, 

- 

' 

275 

00 

260  THE   RATIONAL   ARITHMETIC. 

i.   Make  bills  for  the  following: 

Feb.  4,  Mrs.  J.  K.  Brown  bought  of  White,  Jones  &  Co.: 
10  lbs.  of  Sugar  @        $.05 

20        ''     Flour  @  .04 

2  '•     Tea  @  .60 
Jan.  11.  L.  B.  Hall  bought  of  Smith  Bros.: 

20  pr.  Boys'  Boots  @       $1.75 

15    "    Slippers  @         1.50 

25    "    Ladies'  Shoes  @         2.75 

25    ''    Rubbers  @  .50 

June  4,  Messrs.  Black  &  Co.  bought  of  Marshall  Field 
&  Co. : 

3  bolts  of  Velvet  @  $100.00 

3  "     Muslin  @      37.00 

2  "     Calico  m      10.00 

May  5,  L.  French  bought  of  Browne,  Steele  &  Co. : 

5  yds.  of  Silk  @      $1.75 

3  "  Ribbon  @  .75 
12          "     Gingham  @           .12 

7  "  Velvet  @  4.50 
15          "     Calico  @  .05 

4  papers  Pins  @  .07 
2       "       Needles  @  .08 

Sept.  1,  J.  C.  Hill  bought  of  Birch  &  Son: 

8  Histories  @  $1.25 
15  Spellers  @  .25 

9  Readers ,  @  .40 
12  Grammars  @  .60 
20  Arithmetics                  @  .55 

Oct.  21,  O.  F.  Horn  bought  of  Taylor  &  Co.: 

5  Coal  Stoves  '  @  $20.00 
10  Oil  Stoves  @  8.00 
25  lbs.  Nails                     @  .04 


PART   THIRD.  26J 

1,   Make  out  bills,  supplying  names,  find  the  amounts,  and 
receipt: 

9  lbs.  of  Ham                  @  $.16 

8         "     Yeal                  @  .12 

12         "     Mutton             @  .12i 

16         "     Beef                  @  .14^ 


4         "     Pork 

@ 

.081 

13  lbs.  of  Dried  Beef 

@ 

$.12 

25         "     Codfish 

@ 

.11 

16         "     Mackerel 

@ 

.061 

18         "     Bacon 

@ 

.121 

30  yds.  of  Cassimere 

@ 

$1.75 

70  Spools  Thread 

@ 

.031 

64  yds.  Sheeting 

@ 

.12 

45     "     Calico 

@ 

.04 

5  Table  Cloths 

@ 

2.50 

112  bbl.  Flour 

@ 

$  6.20 

108  tons  of  Hay 

@ 

14.00 

250  bu.  Wheat 

@ 

.92 

130    "    Corn 

@ 

.321 

75    "    Barley 

@ 

.85 

12  doz.  Eggs 

m 

1.121 

12  lbs.  Rice 

ii^ 

.04 

48     "    Coffee 

@ 

.331 

15    "    Butter 

@ 

.22 

32    "    Cheese 

@ 

.14 

6  rolls  of  Wall  Paper 

@ 

$.20 

8  qts.  Paint 

@ 

.30 

6    "    Oil 

@ 

.15 

263  THE   RATIONAL  ARITHMETIC. 

1.  What  part  of  a  dollar  is  50^?     25^?     10^?     1^? 

2.  How  do  you  write  l(p  as  a  fraction  of  a  dollar?     How  do 

you  write  it  with  the  dollar  sign  (^)  ? 

3.  How  do  you  write  10^*  as  a  fraction  of  a  dollar?    With  the 

dollar  sign? 

4.  How  do  you  write  25^-  as  a  fraction  of  a  dollar?     With 

the  dollar  sign?     50^'  as  a  fraction  of  a  dollar?     With 

the  dollar  sign? 
$.01  =  ^Q-  of  a  dollar. 
.10  =  tW  (o^'  To)  of  a  dollar. 
.25  —  y^jj  of  a  dollar. 
.50  =  -^-^  of  a  dollar. 

5.  The  period  used  between  figures  when  writing  dollars  and 

cents  is  called  the  decimal  point. 

6.  It  is  much  easier  to   write  cents  with  the  decimal  point 

than  as  fractions  of  a  dollar. 
1^'  =  yi^  of  a  dollar  =  .01  of  a  dollar, 
10^'  =:  ^LQg-  (or  -^)  of  a  dollar  =  .10  (or  .1)  of  a  dollar. 
25^*  =  -f^  of  a  dollar  =  .25  of  a  dollar. 
50^'  =  -f-^-Q  (or  -^-q)  of  a  dollar  =  .50  (or  .5)  of  a  dollar. 

7.  Numbers  when  written  with  the  decimal  point  are  read 

exactly  as  when  written  as  fractions, 
y^  Q  of  a  dollar  is  read  one-hundredth  of  a  dollar. 
.01  of  a  dollar  is  read  one-hundi^edth  of  a  dollar. 
yL  of  a  dollar  is  read  one-ienih  of  a  dollar. 
.1  of  a  dollar  is  read  one-tenth  of  a  dollar. 
y\^^  of  a  dollar  is  read  twenty -fire-hundredths  of  a  dollar. 
.25  of  a  dollar  is  read  hventy-five-hundredths  of  a  dollar. 
-f^  of  a  dollar  is  read  five-tenths  of  a  dollar. 
.5  of  a  dollar  is  read  five-tenths  of  a  dollar. 

8.  From  this  it  is  seen  that  the  first  figure  following  the 

decimal   point  is  read  as  tenths;    the  second  figure  as 
hundredths. 


PART   THIRD.  203 

1.  Read  the  following  numbers  as  parts  of  a  dollar: 

.05                             .45                             .23  „3 

.6                              .93                            .8  .44 

.18                            .06                            .75  .02 

.72                            .15                            .9  .12 

2.  When  fractions  are  written  in  the  common  way,  by  using 

the  line,  as  ^,  they  are  called  Common  FracUons;  when 

wa'itten  in  this  new  way,  by  using  the  decimal  point, 
as  .1,  they  are  called  Decimal  Fractions. 

3.  Fractions  of  anything   else  as  well   as   of  money,  when 

having  the  denominators   10  or   100,   may  be  written 

with  the  decimal  point.     Thus: 
y^  of  a  bu.  =  .1  of  a  bu. 
^Vir  of  a  T.  =  .25  of  a  T. 

4.  Write  as  decimal  fractions  the  folloAving: 

94                  _4_                  1_5_  6_ 

10  0                10               Too  To  0 

7                   _8_6_                 _9-_  6 

10                 100                100  lo 


4 

To" 

1  5 
To  0 

8  6 

9 

1  0  0 

1  00 

1  9 
10  0 

9 
1  0 

5 

1  0 

1  2 

loo 

_1_8_  . 

10  0  10  0  TT  ]  0  0 

_6_  J)_  12_  2 

10  10  Too  10 

5.   A  boy  spent  .25  of  a  dollar;  how  many  cents  did  he  spend? 

.01  of  a  dollar  =  hj-. 

.25  of  a  dollar  =  25  X  1^'  =  25^. 

0.  From  a  flock  of  350  sheep  a  farmer  sold  .3  of  them.     How 

many  did  he  sell? 

7.  A  piece  of  cloth   10  yd.  long  was  sold  to  two  customers, 

one  baying  .5  of  it,  the  other  buying  the  rest.     How 
many  yards  did  each  one  take? 

8.  A  boy  traveled    100  miles,  going  .2  of  the  way  by  boat. 

How  Etiany  miles  did  he  go  by  boat? 

9.  From  a  cistern  holding  500  gal.,  .07  of  its  contents  were 

drawn  off.     How  many  gallons  were  drawn  off? 
10.  A  man  bought  .75  of  a  quantity  of  grain  measuring  400 
bu.     How  many  bu.  did  he  buy? 


264  THE   RATIONAL   ARITHMETIC. 

1.  Ill  one  dollar  liow  many  cents? 

2.  What  part  of  one  dollar  is  1  cent?     12  cents?     23  cents? 

3.  Another  term  for  hundredths  is  p^7^  cent 

15  hundredths  of  a  dollar  =  15  per  cent  of  a  dollar. 
7  hundredths  of  a  dollar  =  7  per  cent  of  a  dollar. 

4.  Instead  of  the  word  per  cent,  the  sign  ^o  is  often  used. 
15^  of  a  dollar  =  15  per  cent,  or  hundredths,  of  a  dollar. 
Ifo  of  a  dollar  =  7  per  cent,  or  hundredths,  of  a  dollar. 

5.  Since  anything  may  be   divided  into  100  equal  parts,  any 

number  of  such  parts  may  be  called  so  many  hundredths 

or  per  cent. 
^Iq^  of  a  bu.  =  15/^  of  a  bu. 
y^  of  a  bu.  =  7^  of  a  bu. 

6.  Since  lo/h  is  the  same  as  y^^^,  it  may  be  written  as  a  deci- 

mal fraction  exactly  as  yi/o-  may  be  written  decimally, 
.15;  Ifo,  the  same  as  y-J^-  may  be  written  .07. 

7.  Write  first  with  per  cent  sign,  then  as  decimal  fractions: 


8 
10  0 

6 
10  0 

1  3 

loo 

3  3 

1  0  0 

40 
10  0 

1  8 
100 

1  4 

Too" 

1  2 

loo 

25 
10  0 

20 
10  0 

5  0 
100 

1  6 
10  0 

75 
1  00 

6  0 
1  00 

45 
10  0 

66 
Too 

8.   Write  first  as 

common,  and  then  as 

decimal  fractions: 

lOf. 

25% 

64f. 

IW/o 

15^. 

20f. 

53f. 

SS^/o 

3f. 

50f. 

2fc 

16|f. 

5% 

7  of. 

i^fo 

66P 

9.  Write  as  common  fractions: 

.8 

.25 

.7 

.09 

.5 

.14 

.04 

.85 

.16 

.75 

.65 

.01 

.33 

3.1 

2.25 

1.03 

PART   THIRD.  265 

1.  Review  pages  190  and  226. 

2.  How  many  cents  in  J  of  a  dollar  ?    In  -|  of  a  dollar  ?     |  of 

a  dollar?    |^  of  a  dollar?    g^  of  a  dollar?    |^  of  a  dollar? 

3.  What  per  cent  of  a  dollar  is  J  of  a  dollar?     f  ?     -|?     |^? 

5.Q       £9        7.9 
8  •        8  •        8  • 

4.  Instead  of  one  dollar,  find  the  same  parts  and  per  cents  of 

one  gallon.    One  bushel.    Of  any  unit.     Of  $8.    Of  ^24. 
Of  40  marbles.     Of  84  acres. 

5.  2ofo  of  any  number  is  ^  of  the  number. 

6.  Make  similar  statements  regarding   the   other  per  cents 

used. 

7.  How  many  cents  is  J  of  a  dollar?     |  of  a  dollar?     4  of  a 

dollar?      I  of  a  dollar? 

8.  What  per  cent  of  a  dollar  is  J  of  a  dollar?    |  of  a  dollar? 

9.  Instead  of  one  dollar,  find  J  and  |  of  one  yard.      Of  one 

foot. 

10.  What  per  cent  of  a  foot  is  -J  of  a  foot?    |  of  a  foot?    ^  of 

a  foot?     I  of  a  foot? 

11.  What  per  cent  of  a  yard  is  J  of  a  yard?     |  of  a  yard?     ^ 

of  a  yard?     f  of  a  yard? 

12.  Find  16ff^  of  18  pigeons.     Of  24  marbles.     Of  30  boys. 

Find  83|f.  of  the  same.     3Sl%     mi%. 

13.  m\7o  of  12  is  4.      i  of  12  is  4.      33if.  of  12  and  \  of  12 

are  the  same. 

14.  Make  statements  about  the  other  per  cents. 

15.  50/^  of  Fred's  money  is  15  cents.     How  much  money  has 

he? 

16.  75^  of  the  milk  one  family  uses  in  a  week  is  8  quarts. 

How  much  milk  is  used?     What  part  of  the  quantity 
used  is  8  qts.  ? 

17.  83  J%  of  the  horses  in  a  livery  stable  is  21.     How  many 

horses   in   all?     What   part   of    the    whole   number   of 
horses  is  21  horses? 


266  THE   RATIONAL   ARITHMETIC. 

1.  16f/^  of  my  pens  is   42.      How  many  pens  have  I?     42 

pens  is  what  part  of  the  whole  number? 

2.  A  boy  lost  IQ^fc  of  his  marbles,  and  had  30  marbles  left. 

What  part  was  lost?  How  many  were  lost?  How 
many  had  he  at  first? 

3.  In  an  orchard  of  156  trees,  16|^  are  pear,  and  SS^fo  are 

apple.  AVliat  part  of  the  whole  number  of  trees  is  pear  ? 
Apple?     How  many  of  each? 

4.  A  man  bought  a  bicycle  for  $54  and  sold  it  so  as  to  gain 

25/^.      What  was  the  selling  price? 

5.  87i^  of  the  butter  in  a  dairy  is  84  pounds.      What  is  the 

whole  number  of  pounds?  If  sold  at  23  cents  per 
pound,  how  many  dollars  will  the  dairyman  receive  ? 

6.  A. stock  dealer  sold  124^  of  his  horses  and  had  42  left 

How  many  had  he  at  first?  How  many  were  sold?  If 
each  horse  sold  for  $85,  how  much  money  did  the 
dealer  receive? 

7.  A  milkman  sold  24  gallons  of  milk  on  Tuesday,  which  was 

25^  less  than  the  number  sold  on  Monday.  What  part 
of  Monday's  sale  was  Tuesday's?  How  many  gallons 
were  sold  on  Monday? 

8.  Review  1,  2,  3,  4,  page  264. 

9.  \7o  (.01)  of  $100  =  $1.      \%  of  any  100  =  1. 

10.  IJo  of  200  :=  how  much?     If.  of  300  =  how  much? 

11.  Find  ^7o  of  200. 

Vfo  (.01)  of  200  =.  2. 
5,%  =  5  X  2,  or  10. 

12.  In  the  same  way  find  3f.,  4/^,  5f.,  6/^  7f.,  8f^,  9f^  of  200. 

13.  Find  4^  of  90;  6^  of  80;  9^.  of  30. 

14.  Find  10/.  of  400;  20^  of  500;  35^^  of  200. 

15.  Find  25f.  of  600;  50f.  of  250;  75f.  of  800. 

16.  In  what  other  and  shorter  way  may  we  find  25^,  50^  and 

75^  of  numbers? 


PART   THIRD.  207 

1,  A.  man  invested  ^500  in  business  and  gained  1%  on  his 

money  the  first  year.     What  was  his  gain? 

2,  Of  862  feet  of  lumber,  4^  is  oak.     How  many  feet  of  oak  ? 

3,  In  a  school  of  1,400  children,  15%  are  in   the  grammar 

grade.     How  many  pupils  in  the  grammar  grade? 

4,  I  have   80  marbles,   and   5/^  of   them   are   agates.     How 

many  agates  have  I? 

5,  5,824  hours  equal  how  many  days? 

6,  A  grocer  sells  3,690  ounces  of  tea.      How  many  pounds 

does  he  sell?     What  is  the  selling  price  of  the  whole 
amount  at  80^  a  pound? 

7,  A  man  bought  a  house  and  lot  for  $2,000.     After  paying 

$75.50  a  month  for  18  months,  how  much  did  he  still 
owe? 

8,  A  man  sold  25  horses  at  $87.36  each,  and  with  the  money 

bought  land  at  $24  an  acre.     How  many  acres  did  he 
buy  ? 

9,  23  horses  were  exchanged  for  46  cows.      The  cows  were 

valued  at  $45  each.      What  was  the  average  value  of 
each  horse? 

10.  A  grocer  having  $465  wished  to  buy  84  barrels  of  fiour  at 

$5.50  per  barrel.     Had  he  money  enough  to  make  the 
purchase?     If  more  or  less,  how  much? 

11.  How  many  rows  of  bricks  in  a  chimney  64  feet  high,  if 

3  rows  measure  9  inches? 

12.  How  many  bricks  in  a  wall  45  feet  high,  93  bricks  long, 

and  2  bricks  thick,  if  4  bricks  measure  1  foot  in  height? 

13.  How  many  hours  will  it  take  to  deliver  5,400  bricks  if  a 

team  .hauls   500  at  a  load,  and  makes   one  trip  in  IJ 
hours  ? 

14.  A  bricklayer's  hod  holds  20  bricks.     If  he  carries  6  hods 

in  54  minutes,  how  many  hours  will  it  take  him,  at  the 
same  rate,  to  carry  1,200  bricks? 


268  THE   RATIONAL   ARITHMETIC. 

1.  A  man  paid  $115.20  for  144  bushels  of  wheat.     What  was 

the  price  per  bushel  ?  The  wheat  was  sold  at  a  gain  of 
12^fo.  How  much  was  gained?  What  was  the  whole 
amount  received?  At  what  price  per  bushel  was  the 
wheat  sold? 

2.  From  a  barrel  containing  31^  gal.  of  vinegar,  there  were 

drawn  out  at  one  time,  6  gal.,  3  qt.,  1  pt. ;  at  another, 
12  gal.,  3  qt.,  1  pt.,  and  at  another,  3  gal.,  1  pt.  How 
many  gallons,  quarts  and  pints  were  left  in  the  barrel? 
The  remainder  Avas  sold  for  $2.19.  AVhat  was  the 
selling  price  per  gallon? 

3.  Make  out  a  bill  for  the  following,  as  on  page  261: 


12    lbs. 

of  bacon 

at  $ 

0.121 

7    lbs. 

of  ham 

at 

.161 

3|  lbs. 

of  coffee 

at 

.40 

H  1^- 

of  tea 

iit 

.80 

5    lbs. 

of  butter 

at 

.22 

6    doz. 

eggs 

at 

.15 

What  change  should  be  received  from  a  ten-dollar  bill? 

4.  What  will  be  the  cost  of  laying  a  concrete  walk  380  ft. 

long  by  6  ft.  wide,  at  16§^/'  per  sq.  ft.  ? 

5.  If  it  costs  $418.20  to  fence  a  block  369  feet  square,  what 

price  is  paid  per  yd.  ? 


VB  358C2 


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